If someone wants to find out your identity, they're not going to turn to GPT-3, they're going to do the Google search. With that in mind, I don't see how GPT-3 turning up the same stuff that Google does when given your username is a threat to you.

If there's a prompt out there that doesn't contain your username but does spit out your full name, that's a bigger concern.

EDIT: Oh, and as far as bots go: I really can't imagine someone coding their bots to rely on GPT-3 for personal info. GPT-3 doesn't have an "I don't know" answer. In your case it might turn up something useful, but for most people it would turn up nonsense that is indistinguishable from something useful. It's far more reliable and most likely cheaper in the long run to just buy the data.