This is a common concern. The AA traditions fiercely prescribe anonymity,et with humans involved it is not a perfect system, IMO and IME.
Two things from my experience- plenty of people knew about my terrible behavior when drinking, and I would rather them know I stopped and got help than just know that old me. Also, I have met plenty of people I had already thought well of outside of AA, did t know were in the program and went, huh maybe they do indeed have something I want like AA talks about.
Is it possible your boss!sriend would share that you start going? Sure. Should he? No way. Should it really be enough to stop you from going if you need to quit drinking like I did? Your call.
For me, anyone who judges me harshly or looks down on me for being in recovery isn't worth my energy. I first had to choose life over death, literally, and now I choose the. amazing, real, sober life I have over anything, anyone and any opinion out there.