Really? You're worried about her knowing your first name? You know her first name too right?
The scenario was potentially nerve wracking but I'd be more worried about her knowing who you work for/where you work so she could, if so inclined, find out your surname, what car you drive, where you live...etc
Similarly you know where she works and can do the same. It sounds like she played it cool whereas you're being a bit dramatic. Fair play to her for having the confidence to approach you. Hell, she might even have been worried that you were going to bust her since she's giving your boss a hand shandy every week.