When I got sober, something happened that helped me realise I had NO anonymity to give away in the first place. When I was nine months sober, someone at work started a rumour (an untrue one) that I was arriving at work drunk. This helped me to see:
1) The only person I was kidding was me. What I thought was a secret (my drinking problem) was perfectly obvious to everyone else.
2) If someone wanted to use that against Me, they would. They probably had already...but I was too drunk/in denial to notice
3) If I really wanted to stay sober I had to let go of the fear of what other people thought.
I have never had a problem with anonymity in AA in 8.5 years...despite meeting several other members at work, in my circle of friends, and even just passing acquaintances. Other folls in an AA meeting are there for the same reason as me.
P