For E.G in this question, the user is trying to edit his/her question with another account that has the same name.
Should this edit be Approved or Rejected?
This generally happens because they posted the question on an unregistered account and then later registered one when they realized they would need to follow-up on comments. I have yet to come across a case where somebody makes a fake account with the same name to impersonate another user, so you can probably assume it's the same user and approve it, as long as the edit looks to actually be useful. You can also flag these posts and mention that the user accidentally has two accounts, and we can put in a request with Stack Exchange to merge them so their new registered account will take ownership of the question.