I agree that it's a personal choice.
I told everybody and reminded them often but I live in a pretty small town and got 3 DUI's. Everyone here knew about all of it. I told my friends because they were all drunks and I wanted them to know why I wasn't hanging around the old haunts. I told my family because I wanted them to know I actually gave a crap about living.
I had tried quitting and keeping it to myself several times before and it never took. I found that telling people helped with accountability and most importantly helped me accept that I could never drink safely again.