Yes, to the extent that the brothel I use I need to pass a retinal scan to get in....
Your name is fake. The girl knows your name is fake. Her name is fake. You know her name is fake. Why would she possibly ask for id? Why would she possibly care who you are?
And in terms of what she could do with it. Jesus Christ the list is endless. And has been endless for many people who have done it - seriously.
So don't ever give a girl your real name, or real info about you. Ever no matter what.
When you have been punting for a while you will realize how utter crazy your question has just been.