Wow. Lots of reasons not to ring the bell after getting sober. Early on, it can be too much pressure in the sense that we're changing (or, worse, attempting to change) people's perceptions or experiences of who we are. In this way, we may also raise both others' and our own expectations around who we now are as a self-proclaimed sober individual.
Would I also let people know that I'm no longer a pathological liar, that I've stopped shirking major responsibilities in order to drink or that I've ceased driving when I'm drunk? That I've stopped sneaking around and stopped making poor excuses for my bad behavior?
It's not really about the drinking; it's about how I behaved while I was drinking, including the times when I wasn't actually drunk. I made myself reliably untrustworthy, and my company was universally unwanted. I said things I couldn't take back, and did things that left wounds that no amount of amends could fully heal. We cannot unhurt people, no matter what we say or do. Sobriety, for me, has been its own reward, and I don't need to be congratulated for cleaning up what I say and what I do. Also its own reward. (And I'm not suggesting that any of these things are what motivates you,)
I had no desire to tell anyone that I'd stopped drinking when I first got sober, and in the almost five years since I put down the drink, I have yet to encounter an experience in which it would have been helpful for me to do so. Even though I don't often know it, I influence people by what I do, and not by what I say.
Finally, the people who I've admired most in life are generally those who shine quietly, avoiding the well-deserved spotlight, and accepting life as it comes, rather than attempting to change it based on their own fears.