I don’t really keep up with Dooby so this is a genuine question - do you have a source for this? I’d love to confirm it from her rather than taking it on faith.
It’s in her Debut stream (1:01:15 if the timestamp isn’t working)
And as far as I know companies don’t forbid talents from talking about that stuff at all, people like Dokibird would be sued to hell and back if that was forbidden. A lot of talents (Kiara, Matsuri, Noel for example) have accidentally called themselves with “the wrong name” on their PL account and nothing happened afaik. The only thing I know is forbidden is to bring official hololive material into private streams, like Aloe/Delutaya accidentally did.
Dooby never explicitly said her name on stream, as far as I know. While “bragging” she even said “it doesn’t matter, you guys are gonna find my name anyways”, so it felt like she didn’t even really want people to find out. I don’t think that’s “deliberately making it public”.
And about the main topic, I’m actually pretty sure that they could talk about it if they wanted (like Dokibird did, although that was Niji), they just choose not to because… what would be the point? Pretty much everyone who watches Dooby/Keeki/Kson and the likes knows who they are/were. I just see it as a way to “separate” the two environments, not anything that’s actually enforced. It’s not like anyone wanting to hire Kson wouldn’t know about her past anyway.
What is enforced is the reverse, they can’t talk about private details on Hololive streams (and that’s why Ame couldn’t talk about the Emmy or her parents being cuban), but that’s just to “keep kayfabe” and avoid stalking issues.