It's your call. Everyone has their way of self-identifying. I have heard all sort of different identifying at meetings, but 99% of them will identify with "I'm X and I'm an alcoholic". People dress it up however way they want - doesn't matter to me, and it shouldn't matter to you. You will certainly hear over and over the whole "recovering" vs "recovered" argument (they pop up on SR now and then too), but it's however you feel comfortable.