There is no answer written based on Stack Exchange perspective. So, I am writing an answer covering all the possible ways available in front of us. It is long.
The major argument you have listed in the question is hovering the tag excerpt and wiki.
1) It's only in the desktop and laptop one should hover to get tag description. There are thousands of mobile users (like me) and for them hovering doesn't work. They have to go to the link of 'Mythology' tag itself open a new page and read there, which one rarely does.
This is not in our hands. This is a feature something the Stack Exchange should look into. SE is mainly intended for desktop and laptop users. So, the main focus will be on that users only. Many features do not work on mobile site or the app. If we have to get rid of the tag just because a certain feature does not work on mobile or app, we have to get rid of many things on the site which is not going to happen. There is feature-request on Meta Stack Exchange Allow access to tag wikis from the Android app to access to tag wikis. If that gets a status-completed on it, we can think of this argument. For now, we need not to remove mythology tag due to this reason because we do not have any role in implementing a feature.
If the tag should be removed due to this reason, we must have to remove many other tags because their excerpts and wikis are not visible and not many would take their time to see what the tag means. So, we have to remove many tags whose names are complex to understand or not known to many. E.g health, pramana. If one looks at health, they might decide to post a new question about their health (which we already did). So, we would be receiving many off-topic questions. So, we should remove those tags too. Should we? I will leave that question to community.
The question tagged with 'Mythology' in google search show with 'Mythology - question' format in this case also hovering doesn't works.
Not necessarily. According to answer to How is the tag chosen to prefix the title? , the popular tag in the question takes prefix into the question.
It's the most popular tag that doesn't already appear in the title.
In your example, PHP is mentioned in the title so the second-most popular tag "nginx" is chosen for the HTML title.
So, it is based on HTML title of the page. We should not bother what is shown in the google search results. They change from time to time. If our tagging policy changes based on new trends on google, we should change our tags and their names every month. It is help center and meta which decides how a tag should be used. Burnitating a tag and creating should be based on discussions and not on Google results. When I was randomly searching for our site, the results were the following:
And today, they changed.
So, my point is simple. We should not be bothered about google search results which change day to day and tag based on what is shown as prefix in results. That should not be our concern.
Even if it shows in the format mythology- question, what would be the problem? Tags on our site do not indicate the authenticity of the topic discussed in the question. They indicate the topic. We should not use to indicate correctness to questions and answers. Due to this format, we might have to see some questions as "sin- question name" format. So, does that not mean we are supporting evil intentions of sin or crime in internet users. All tags are equal in this matter let it be ramayana, puranas, ravana. It is just the title of the html page which is based on page source and takes whatever it sees as popular tag. So, this is also a an invalid argument for removing a tag in a question. We should be tagging based on the topic of the question only and not to show the question or answer is right or wrong. Tagging to show factual correctness would make the site biased towards religion or against religion. But we need a neutral environment for everything.
Should we remove the tag completely? No. Currently we are using the tag for following reasons.
For questions about stories that are part of Hindu religious beliefs. Hindu mythology can be found throughout Hindu scriptures like the Vedas, Puranas, Ramayana, and Mahabharata.
So, we are using the tag for stories only. Not to denote that the stories are false. Due to the emotion and sentiment, people are not adding the tag. There seems to be a partiality in adding the tag for related questions which ask for stories too. Even if it is added in edits, that is forcefully removed. This is a dangerous situation. A user should be free to tag a question based on the topic of the question. If the question asks for a sin, we are tagging at as sin. If something related to lust and anger, we are tagging as desire or kama. The word Kama has a very bad connotation in general usage and common people. What can be worst than that? But we are still tagging that if the question asks about that topic. No tag removals are being made. So, why should be there a partiality in adding a tag about stories? There should not be removal of tag which indicates stories. Stories are very important in Hinduism and that differentiates questions like philosophy, finding source of the question, asking nature of text or asking interpretation of a shloka or a passage. We are adding a separate tag for each of the topic. So, there is no harm in having a tag which denotes stories. This will also help the users to find related questions easily. The original purpose of the question is also the same:
A tag is a keyword or label that categorizes your question with other, similar questions. Using the right tags makes it easier for others to find and answer your question.
So, if someone is interested to read questions about stories, there should be a way they should find and having a tag is the solution. So, the tag should not be removed.
Another solution proposed is tagging as itihasa or purana. This does more damage. This spoils the usage of those tags. Even though itihasa means "as it happened", it is not used in that sense every time. When itihasa is used, Ramayana and Mahabharata are also referred. We are using that tag which includes both the texts and which asks for the nature of itihasas only. Using that tag for stories assuming every story is from itihasa because every thing happened literally gives rise to bias. Itihasa in Sanskrit translates to history. But when we use history, it denotes how Hinduism developed in historical context over millenniums. It is used to ask about history of Hinduism. So, using it as a substitute of mythology is also not a good idea. We are using puranas as a general tag when it is nature of puranas or it generally concerns with puranas. Not every story finds place in Puranas or itihasas but believed strongly to be happened. We can find examples of thousands of stories as sthala puranas (temple legends) and folk lores which are not present in primary texts but popular in oral tradition. So, we need a tag which covers all the stories. Important thing is we should not treat these stories as completely false because it is a matter of belief.
Another argument made:
our itihasas (iti-hasa - like so, it was) are history, although quite old to the point that people don't believe them, just as people don't believe in jesus or pretty much anything before the invention of photography, or anything after the invention of photoshop.
True. There are people who believe in something and do not believe in something at the same time. Even if we take some incidents from itihasas or puranas, some are very hard to believe. A chapter in Bhavishya Purana (a major purana) says the army of kings in 12th century had millions of soldiers each side. If not million, crore. But if we look at the population, this may not match with history. So, it is based on personal belief. As a site, we should not be dictating it. We should be as neutral as possible. A tag should not indicate whether the incident has happened really or not. It should not mean different things to different people.
If it is meaning differently to different people, it comes under a meta-tag. Meta-tags are discouraged on Stack Exchange sites. From The Death of Meta Tags
If the tag commonly means different things to different people, it’s probably a meta-tag.
So, we as a site should not step into personal beliefs to solve this matter. We should be as neutral as possible. We should define in the tag excerpts and wikis what it means to our site. We as a site has a policy which would not hurt the feelings of any religions or classes. So, it is obvious that we do not use mythology in a derogatory form.
The only reason to think of this discussion is the name mythology having a bad connotation on the internet. Seems a valid reason. We have to consider that we look at all the tags equally and do not show any tag based on the questions. There are many other tag names which have a bad connotation or an ambiguous meaning. For example. look at sex. health, divorce etc, which are not related to Hinduism at all. These are controversial terms too. So, what about connotation of these tags? Should we delete aforementioned tags too?
If the problem with mythology tag is number of questions asked and damage it is doing by being the top tag, that is not the problem we should be bothered about. People are more interested in stories and asking questions on it.So, we should let them. Interests change time to time. After a few years, people may be interested in some other tag and number may increase for that tag.
What is a top tag and stats of tags are not shown to a passerby user. These are only shown to users when logged into the site. If the users are already members, they are expected to read the excerpt and wikis and tag based on the topic by following it. For a passerby, it doesn't matter if it is a top tag or anything. So, we should be clear what we mean by mythology here. If you are wondering mythology being the top tag doesn't alter the passersby or internet users, the answer is no.
The tag is not showing up in google search results at all. Surprisingly it is sex which is showing up even though it has very less compared to mythology or scripture. So, deciding and discussing our policies simply based on internet results or opinions on internet people would not be a great idea.
If we are going through the popular usage and connotation in society and internet, we must have to make major changes to our tagging, Q&A style and almost everything. Varna is almost synonymous to Caste now. But originally, both of these are different. We have different tags for caste-system and varna preferring original meaning over popular meaning formed due to incidents. The same is argued and written in Q&A that varna and caste are different in the religion. Besides these, "varna" has a wide range of meanings. Which meaning to be taken on which context is also decided and best meaning is taken into account. Varna also means color. So, if we tag a question with color (one of the popular meanings), we are not talking about color or complexion. If a passerby understands it as talking about a color or race, we should make it clear what we are talking about. I think we should go with a similar approach with this tag too.
Myth originally meant:
"a traditional story, especially one concerning the early history of a people or explaining some natural or social phenomenon, and typically involving supernatural beings or events."
In more detail From an answer from Christianity.SE regarding the original definition of myth and mythology:
The word myth, in its academic definition, means a story with deep power and symbolic meaning. When studied in the academic sense, it's that meaning that is important, not whether the story actually happened or not. Thus ancient 'myths' like the founding of Rome, or the stories of Hercules were important (to their societies) for what they said and the effect they had on those societies rather than because of their historicity.
Many of those myths turn out not to be actually true (like Hercules). That doesn't necessarily rob them of their power. The existence of the story can still shape a nation and a culture. But given that they mostly aren't historical, the word 'myth' in common parlance has come to mean 'something that isn't true' (giving rise to 'Mythbusters' for example). But that's not the sense that Lewis, as an academic, intended it.
Hence the original meaning when used in academic sense means a story with deeper symbolism. That is how the word originally meant. But due to changes, the meaning has changed like many other terms. But we on the site are following the original meaning over current popular meaning. So, why not for this tag too?
So, I have so far covered pros and cons of using all the ways mentioned in the question and some of the arguments which rose up during the discussion. I have answered from a Stack Exchange perspective and academic perspective without showing partiality towards any way i.e., removing or adding the tag till now. So, I feel we should not follow way 2 at all. We should also not tag it indicate beliefs because we are not a Hindu site. There should be neutrality in all regards as much as possible. Hence using wrong terms and tags like Purana or history as a substitute for mythology is also not preferable.
Now we are left out with adding a tag excerpt and wiki clearly what we mean by a term (in the case of varna or other ambiguous tags). And renaming the tag. If we follow the above way striking out the issues of passersby users & internet opinions, removing partiality towards a tag, we need to rename the tag. We just need to be clear in the tag excerpt and wiki that we do not mean we are using the tag in a wrong way.
After this discussion was posted on meta, one of our moderators Pandya posted question on ELU on what is the best alternative for mythology. For that, there were some responses which are noteworthy.
My guess is that all synonyms of "myth" or "mythology" are going to create equally big or bigger problems. Mythology is really the word you want. If you are looking to emphasize the sacredness in order to avoid misunderstanding, maybe use an adjective. Consider tags along the lines of sacred-mythology.
I think the word mythology is your best bet, precisely because it strikes a balance between the camp that holds these stories are historical and factual and those who hold them to be instructive but apocryphal. Any words which does have this "ambiguity" (really, neutrality) is going to put off one of these camps or the other, which defeats the purpose of the exercise.
If we are not convinced that mythology is still bad after reading complete answer (you really read it completely? ;-)), we are only left with renaming the tag with something which is close to stories which do not indicate beliefs or historical accuracy. Usage of other terms like narrative, tradition etc., would be more misleading than the present term. So, the word mythology or sacred-mythology would be my suggestion to solve this. It will bring a balance between users without affecting their beliefs. It also reflect the academic sense (learning about Hinduism without preaching it) and neutrality of the site. Adding a sacred word also shows that we are not demeaning the story or the incident mentioned in the question. Even though we are not a Hindu site showing partiality towards Hindus and opposing other paths which do not have problem with academic use, We are a site about Hinduism after all. Why would we use derogatory term? We only mean the word in a good sense. All the best and cheers! Let's hope for the best.