R these good names? ? ?

I personally like both of the names. I think the name Alexandra is beautiful and you can go by Alex or Alexis if you wanted. When I think of Carmen I think of Carmen Electra who is gorgeous. So out of those two name Alexandra is my favorite. But the decision really is 100% yours and you need to make sure changing your name is what you want to do before you go make legal action. Good Luck with your decision.