It is very disappointing when you (general you) realise you can’t fully trust someone. The thing with thinking you should have said “I’m not comfortable with giving his last name” is hindsight talking. We can always be wise after the fact, and do things differently if the situation arises again.
Do you feel like you complied with her request because you felt like saying “no” would have felt like you were being mean or rude? Setting boundaries with others can feel like that, especially if we’ve been trained to please others (not saying that is the case with you, because I don’t know you). Apologies if I’ve missed the mark, it’s just how I read it.