All this buddhist mumbo 'don't be attatched' et cetera is all good and well for helping you overcome annoyances like these, but that doesn't mean you don't take any action at all for what YOU want.
She is obviously not in the best state of mind if she is acting like this. You should have just outright told her straight away you feel uncomfortable with her changing her name to yours, and that it is a strange idea. Not with anger or anything, just tell her your thoughts. Surely she would have shyed away from the idea instantly?
Yes acceptance is good - but don't let it overcome you from taking action.
You will get frustrated with her having the same name as you often.