I quickly learned by going to AA meetings for just a few months in the very beginning of my sobriety that "anonymity" was not gonna actually happen.
It's people. People talk.
I had a long-term neighbor who went to AA for 25 years but she didn't go to meetings in the area, she drove 20 miles to a meeting once a week. She did that because she was in a customer-facing job and didn't want to have to have that overlap between work life and AA. I mean, it's inevitable if I hit meetings near home or if I lived in a less urban location that I would have the same worries.
Part of what bothered me about AA is that intrusion of privacy. I stopped going for a lot of reasons, but identity disclosure was one of them.
Some people that doesn't bother. Me it did.