I read a question in https://math.stackexchange.com/ and notice a username in the bottom-right-corner. It is the name of the person who asked the question? Not necessarily. It is the name who answered the question and it was accepted? Not necessarily. It is the name of the person who (re)edited the original question? Not necessarily. I think it must be name of the person who asked the question. Is it possible to configure stackexchange in this way?
I believe that the name is the last person to edit the question or one of its answers. Editing a comment will not move the question in the queue or change the name in the lower-right corner.
Added: As Martin Sleziak comments, what I say above is true when viewing the "active" tab. Viewing with any of the other tabs seems to show the author of the question.