I think the bodies tag name could be improved: perhaps bodies-tvseries, but when I try to suggest that I can suggest a change to the tag description, not the tag name.
Do I need an additional privilege to do this?
Am I on the right track about a tag name that is too ambiguous?
The moderators have a tool for merging tags, which allows us to automatically change tag-A to tag-B on every question tagged with tag-A without needing to edit them. If tag-B doesn't already exist in the system, this is essentially renaming a tag from one name to another. It's quite a dangerous tool, as it silently changes a lot of posts and it's not reversible, so its use is restricted to moderators only.
Ask on meta. This is the best option if there's any possible doubt or room for argument, but not really necessary if it's a very obvious thing like an actual typo in a tag name.
Flag for mods. If it's an obvious case involving a lot of posts, we'll be happy to do the merge/rename and avoid bumping all those posts with edits.
Just edit the posts. This is fine if it's an obvious case involving very few posts (like 5 or less): you can simply edit out the old tag and edit in the new tag on every post yourself. But this won't work if the tag names are too similar, like just a single character difference: the system will assume you mean the old tag and diamond mods will be needed to change the name in that case.
I agree with you that bodies isn't a great name for a tag applying to a single TV series: we'll have people misusing it for any question about bodies. But I also agree with DavidW that mashing tvseries as a single word doesn't look great. You could either call it bodies-tv or bodies-tv-series. (Looking at the tags list and typing tv into the search box, you can see that both of these options have been used before for other tags.)
You might want to get consensus here first, before making the change, though I agree that's probably a useful improvement.
But as to actually performing the change, you don't change the existing tag, you replace it. You have enough reputation to create new tags, so just type "bodies-tv-series" in the tag box and remove the existing bodies. This will create the tag, and then you can copy over the tag description from the old tag.
The existing "bodies" tag will be removed after a certain period of time in which it is no longer applied to any questions.
Note that I do feel that "bodies-tv-series" with a break between "tv" and "series" reads better than "bodies-tvseries" with them run together.
