It would be nice if it were possible for users to go to Special:RenameUser or perhaps Special:Preferences and put a request in for a rename that would sit in a queue for bureaucrats to review.
While in the queue, the new username would be blocked from creation by outside parties to avoid vandalism issues that have been happening lately on en.wiki (i.e., people creating accounts after they're requested publicly). The bureaucrats would then be able to examine the situation and either accept or reject the request.
Filing under Special:RenameUser as it is the extension currently used, though perhaps this would require a separate extension.