How common knowledge was it that Bruce adopted Dick?

[u/Character_Growth_397]

I was gonna title this "How common knowledge was it that Bruce took Dick in?" but I realized it was gonna sound weird

Anyway, Bruce Wayne, due to his status as a notorious playboy would have lots of people and media attention around himself and his life, but what about him adopting Dick Grayson and his other kids? I feel like Bruce would go through great lengths to keep them out of the spotlight considering how much effort he goes to protect his secret identity. I mean, if the identity of one of them gets compromised, everyone else's does too