It sounds to me like he's doing the empathy thing and working on relationship building. You said you're uncomfortable in crowds. Maybe he isn't himself, but his g/f is, so he's putting it out there as a way of saying that it's not uncommon to feel that way and he understands. Maybe because he's male and you're female, it makes more sense to show empathy through his g/f rather than himself. Or maybe he's had a bad experience with a client becoming romantically interested in him and you're gut feeling is right - he's making sure you know that he's involved with someone. Who knows? There could be lots of reasons.

Why does it bother you that he has brought her up at least once in a dozen sessions? Not saying there's anything wrong with it -- at all -- but it might be worth looking at. My T self-discloses a lot as part of r/s building - mostly about himself, but sometimes about other people he knows, including his wife. All as a way of showing empathy with me.

If it continues to happen and to bother you, you might want to bring it up. The stuff that's hard to talk about is often where some work needs to be done. Good luck!