So - I think it's so stupid that having a drag queen on has become the thing. But, tbh, I think it's kind of a fad. It used to be the thing to have a camp gay man, or a lesbian, and I suppose that's not edgy enough anymore. (And I am not saying that there should only be straight people, but these shows are very typically tokenistic about their contestants.)
But as far as the name: it's crass and vulgar, but I think there is already precedent for this sort of thing on mainstream tv etc now. The one that comes to mind most obviously is the band Hole. The name was meant to be edgy 30 years ago or whatever, but now it's just out there, I am sure many parents listened to their music and would be happy to talk about it with their kids.
Which I suppose goes to show, when it becomes a thing to push what is edgy, in 30 years time it will just be part of the general culture and not edgy any more. So better think about whether that is a good idea.