The only time where it matters at ALL why you're at an AA meeting is if it's a closed meeting. Closed meetings are open only to those who are alcoholics OR someone concerned about his/her drinking (however they would describe it). Open meetings are open to family, friends, anyone who is interested.
You can just give your first name, or say your name and that you're concerned about your drinking, or whatever seems most comfortable. I don't feel in the least uncomfortable identifying as an alcoholic, because the Big Book defines it as someone who has an obsession to drink when he or she isn't drinking, and has the craving for more once any alcohol is consumed. That pretty much describes me, so I got no problem with it.
A lot of people have this image of "alcoholic" as being some skid row bum. All it means is that you have an abnormal reaction to alcohol. No moral judgment implied. And everyone at the meeting uses the term that way, too, so it isn't as if anyone in the room will be looking down on you!