I struggled with this too.. the forever alcoholic/addict thing.
I don't label myself really. I know I drank way too much, and needed to stop.. so I did. now I'm a non-drinker. I don't need to label myself to know how easily it would be for me to slide into again. I guess I was 'addicted' to cocaine too, for like a year.. and quit doing that about 10 years ago. I don't consider myself a cocaine addict now.. but of course I'd never use it again.
I know I'm one drink away from the hell I was living 13 months ago. I know better than to claim any sort of 'power' over that risk.. so I don't risk it. I will never feel so far away from that last drink to ever think I have all the power. Does that mean I label myself something forever. eh.. it's not helpful to me. I'm a non drinker, and I don't use drugs.. I'm just me!