I was speaking with someone from AA today, and he brought up the "anonymity" subject.
It's up to each person whether or not they want to say they're in Al-Anon or AA - so yes, don't go talking about who else is in the room, or what they said. Anonymity is also to be applied towards TV, radio, movies, and any other "public" forum.
But his AA group is of the opinion that if you remain anonymous to the people around you, you're not continuing forward with the intent of the program, which is to reach out to help others. He feels if you don't put it out there, people won't know to reach out to you when they don't know where else to go. Al-Anon is not as well known a program as AA, either.
That said, there's no need to advertise until you're ready, and no need to shout it to the rooftops or anything. It's different with AlAnon, versus AA, as the alcoholics are a bit more obvious. (His example? When he informed his neighbor he stropped drinking and was going to AA, the reply he got was "I know. You stopped parking your car in my flowerbeds and peeing off your roof, and today you're mowing your lawn for the first time since I've known you. I figured something was different.")
I figure it's up to each individual who they want to tell, and when. There's no need to advertise, especially if you're still at the beginning of the program, but at some point you won't be afraid of what others think, and will start telling a little bit at a time.
I just figure I'll know when I'm ready.