I found that telling people I don't drink anymore was much less dramatic than I expected. There was no standing on a podium and declaring through tears: I am an alcoholic!
It truly was more if a nah, not tonight, I'm not drinking or i'm not drinking anymore. there was of course a bit of a white elephant in the room because they knew I drank way too much and way too often.
This was followed by actions and simply not drinking.
A few months in, I actually told them I do not drink anymore and said it firmly. Looking back, there was no reason not to do this right away.