Leaving aside the cultural appropriation and misogyny issues for a moment (not for good, because they are important) - why did/would this person go on a cooking show in character/costume in the first place? Were the other celebrity performers also dressed/in character as their characters? Would, for example, Suranne Jones come and cook dressed as Anne Lister? Or Andy Serkis as Gollum? Would Mila Kunis to stay offscreen and project a cartoon hologram of Meg Griffin? Those would be the equivalents, and some of them would make it very hard to cook safely.
Purely anecdotal: I used to bartend in the Castro (San Francisco) circa early-mid 1990s and we had drag acts perform most weekends (all queens; I don't think we ever had a king - how many kings get a fraction of the attention, exposure, and money even now?) They were/are professional performers, playing a character on stage. When I had to interact with them on business or even when they were having a drink after their sets, I dealt/chatted with (for example) "Matt Smith", not "Jayne Mansfeeled". When Matt stopped in on a day off with some friends, he didn't dress up as Jayne. And I'm sure he didn't wear Jayne's clothes and makeup or use those mannerisms and voice to, say, attend a parent-teacher conference or his sister's wedding or to take his books back to the library. It was (is) a job, not a lifestyle, let alone a full-time personal "identity". And certainly not reality.
As for the names - sure, Cheryl Hole could be a one-off or have another "inside joke" meaning or even be a real name. (I went to school with a Richard Head; it happens.) But it's part of a really obvious widespread pattern that still exists and is problematic even if this particular queen really is the child of Mr. & Mrs. Hole. Back in the '90s I do not remember the type of names we see now that refer overtly to sexual paraphilias or viciously attack and belittle women as a group/class. The '90s queens had fun names that often referred to their "queerness" (as understood at the time) or outsider origins, or with the idea of glamour and aesthetic/sartorial excess: Pollo del Mar, Holatta Tyme, Glamamore, Cookie Dough, Doris Dazed, Fauxnique.
If anything the Kings - those few that were around even if not getting to perform at choice venues - were a little raunchier: Dick Dejour, Rod Lancet, Alex U. Inn, Fudgie Frottage. I sometimes wonder if there's some false equivalence going on now among nonwomen and nonfeminists thinking that these newer super-sexual queen's names are the eqivalent and ignoring the impact of the structural and systemic power differential between men and women and the way it so drearily often colasces around and manifests itself through heterosexual sex and (the normalisation of) sexual violence.
StaunchMomma: Maybe it means bum hole because he's gay? Oh no you did NOT!!!! Think you're reaching to take offence here a little. Think you're reaching very hard to GIVE it. 🙄