Disclaimer: All names contained in this post have been deliberately made public by the person themself.
Model makers, riggers, musicians, artists, and all others involved in the making of vtuber shows are all carefully credited, since it would obviously be reprehensible not to do so, but the actual performer that portrays the Idol goes entirely uncredited. The performers are all experienced entertainment industry professionals, Hololive does not and has never contracted unproven talent. Most of them have IMDB pages but universally their biggest and most prestigious work is not listed there, because Hololive forbids it.
When Rebecca Cardenas went independent as Dooby one of the very first things she did was make her identity public specifically to take credit for some previous work she's done. But even after going independent she is still seemingly contractually prohibited from taking credit for portraying Ame, something that might actually be illegal in my opinion. Rebecca should be able to list her time portraying Amelia Watson as part of her professional work experience.
I am not saying that all the talent should be forced to make their identities public, rather I think they should be credited by a name which they control. For example, the performer portraying Takanashi Kiara does not own that name and could not use that name when doing other work, but she does own the name Keekihime. So while some talent, like Karen Calanni playing Mori Calliope, would want to be credited by their real name, others, like Keekihime, might rather be credited by a stage name. The important part being that they control the name themselves and can use it as they wish.
Hololive refusing to credit the performers unfairly shackles them to the company and inhibits their professional careers, and that's messed up
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.