I don't have anything to add to what's said already, except to show solidarity with you. I'd be upset if my partner shared my sober status publicly without my permission.
Pardon the analogy, but it's like the scene in a recent movie where a main character is proudly gay, but gets really angry when a friend outs him. Their conversation is like this:
"I didn't think you'd care, because you're so okay with it."
"I am okay with it, but it's MY story to tell, not yours."
I'd explain that your sober status is something personal, something that you are happy about, but it's your story to tell, not anyone else's. If your partner wants to tell someone, he should ask your permission first. Ideally, some gentle education about how this is personal should set him straight.
If he keeps sharing with people despite your request, then he's got problems.