Don't worry about it. We surgeons take it all in our stride. 😉

You did well and didn't fuck up.

As a woman, I'd be creeped out by someone who chats me up while I'm working out and asking for my name. Not the time and place. Talking about a relatable experience like that is fine. Don't make a point of chatting every time you see her, say hi but move on. Small talk from time to time. Get to know each other slowly. Eventually, you'll exchange names. Good luck!