As with an 12 step program, the "anonymous" in the name refers more to who and what you see and talk about within the meeting itself.
No matter what kind of meeting you go to, you will never be forced to speak if you don't want to. However, if you do want to share something, the traditional way to introduce yourself is to say your name and who you are to the group.
Some people who have friends or family that are addicts, but are not addicts themselves, also go to meetings, so they would not introduce themselves as an addict.
This is just a suggested way to introduce yourself, but you dont have to say anything at all if you don't want to. You can just share your thoughts without saying your name.
Anonymity and Confidentiality - What Happens In The Group, Stays In The Group
In the group, you are promised - and promise - anonymity. This means that anything you say does not leave the room, which creates a safe environment that encourages people to speak out.
How Anonymous Is It?
As anonymous as you can get without wearing a disguise! For example, if I ran into my boss at a meeting, and admitted that I drank or got high last week, she couldn't repeat anything at work, or say "Guess who I saw at AA?!", or even punish my behavior.
They even have a saying at the end of most meetings that goes something likes "what you see here, what you hear here, so shall it stay here" and then eveyone all at once replies with "HERE" to agree that they will respect the anonymity of each person present.