IIRC the "Zero Punctuation" name was something The Escapist came up with, as is the music and titles. Anything Croshaw created while employed by The Escapist, they own, which is standard.
I'm sure he can still make videos with the same art style, but he can't call it ZP and he can't use the music or intro/outro cards. IIRC he got dinged pretty hard back when he was just a goon making these videos for fun, as he used copyrighted music for the intros, including A FUCKING BEATLES SONG (Octopus's Garden) in his review of BioShock.
I think it's understandable to just want to make your dumb videos and have money, taxes, benefits, promotion, etc. handled by someone else. That shit is a pain in the ass to wrangle on your own.