I've come across edit-mode. It is similar to object-mode, but rather than being a separate tag, it is currently a synonym for editing. since Edit Mode is a specific mode that Objects can be in, it's no really the same as editing, which can cover editing topics other than those applying to objects.
We can discuss whether it's too late to change the tag from a synonym, and perhaps I should ask a question specifically to do that; but for this question, I'm focusing on the general case of editing synonyms.
EDIT: clarification in response to an answer.
So the question is, "in general, if one wanted to edit a tag that is already a synonym for an existing tag, is it possible to modify the tag wiki so they are no longer synonyms, and if it is, what is the process for the Blender StackExchange?"