I’d go with The Gaydar Gay Bar.
Depends on the vibe you’re going for. If it’s a macho sports bar feel i’d go with The Man Zone. Roosters has more of a Southern flair. Or if you’re trying to be trendy, Eggplant.
If it’s a loud techno joint you could call it Jammers.
A little OT, but a guy in Israel wanted to call his bodega after a word he’d learned in the US, “munchies.” He tried to spell it as best he could, and ended up calling his place “Man Cheese.” He had a sign up with English lettering, and everything. Fortunately, the Hebrew sign literally said “manchies,” it didn’t have the Hebrew for “Man Cheese.”
But you might just get a lot of really happy people there.
No, nuts ON the bar, not nuts AT the bar.
I think you’re confused, No Nuts is the lesbian bar.
I agree with other comments that the name ‘Utopia Planitia’ has no connection to a gay bar (and although I’m a Trekkie, I didn’t recognise the reference. 
)
I suggest that the name should hint at welcoming gays and also attract customers in general.
So how about:
Full Howse beats a Straight
This combines 3 objectives:
- it attracts poker players
- it has a subtle reference that something is better than being ‘straight’
- it has a deliberate misspelling*
This will lead to the following conversation - repeated many times:
Walk-in “Excuse me, but your sign is wrong.”
Barman “Thank you for pointing that out - what can I get you?” 
Do I understand that gay bars are going away? I have not seen any numbers, but I have read people who were very upset that gay bars were less-needed in a new more welcoming epoch.
Man Cave sounds like some sort of gay bar.
I’m glad I’ve never encountered the term in person. If anyone ever asked if I wanted to hang out in their man cave I think I’d need to have the “I like you as a friend” speech ready.
Let’s think.
Just to be a little confusing, how about The Wondering See-Men. I thought this was the place for good sea food but looks like some sort of pick-up joint. Should have gone to the Rod’n and Reeling instead.
I’d go with Blue Oyster.
“Peckers.” Like Hooters, but with men in tight shorts serving food and drinks. And a woodpecker on the logo.
How about a ray-finned fish on the logo? You could call it The Bay Gar.
I’m just loving this thread. Gives lots of folks a chance to exercise their “funny” stereotypes and prejudices without any blowback (so to speak).
Most of the gay bar names in Seattle are pretty unremarkable: Neighbors, R Place, Wildrose. The big exception is the Cuff; it’s got handcuffs in its logo and it has no windows, giving you a pretty good clue of who it’s aiming for. Even the local gay bathhouse (yes they still exist) gets the bland name Z Club. Then again, most clubs in this very LGBT friendly city are de facto gay clubs.
Adam and Steve’s.
We used to live a couple of doors down from, “The Manhandler Saloon,” in Chicago. Absolutely no question or ambiguity about the nature of the establishment. 
Or Adam and Yves’s?