You don't have to use the "A" word unless you want to. Telling people is mostly about having accountability. I've gotten the same by telling my friends that I'm not drinking. But I'm not yet OK with using that word with them. I accept it for myself. But I just feel like it has so much cultural baggage that I'm not willing to shoulder. I don't want to give people a short cut in how they think of me. It's enough for them to know that I wasn't happy with how much I was drinking before, and now I've stopped for an indefinite amount of time.
What you want to avoid, I think, is trying to quit entirely in secret. I've tried that before and it didn't work. When I started I told everyone around me that I was quitting for 90 days. When I got to 90 days, I just said I was going to keep at it for a while. That way I still can't get away with drinking, but I don't have to (yet) have those big deep conversations.