One of their best known songs is called “Too Drunk To Fuck”, and someone created a parody band called the Ted Kennedys whose song was titled “Too Drunk To Swim”.
Along similar lines, I’ve always liked ‘Casiotone for the Painfully Alone’, both the name and the band. But my favorite is probably ‘Ostzonensuppenwürfelmachenkrebs’, translating roughly to ‘East Zone (Soviet Occupation Zone, GDR) soup cubes cause cancer’.
I once went to a show at Eugene’s WoW hall just because I had to see what the hell kind of band SWEATY NIPPLES was. Never found out , cause the Cherry Poppin Daddies opened for them, and I immediately fell in love with them and left when they were done. 
There was an Australian band some years ago called People with Chairs Up their Noses. Ok, so they were humorous try-hards. But they had changed it from North 2 Alaskans (they were a duo) which was seriously cool.
One of the best-known bands in Australia (and very good, too) is TISM - This Is Serious, Mum.
Milking the Goatmachine - I almost have to see the band just because of the name.
Jena Malone and Her Bloodstains would be a lot more hysterical if it didn’t actually feature Jena Malone.
There was a relatively famous band in Spain around the 1980’s whose name was “Tarzán y su puta madre buscan piso en Alcobendas”, which translates -more or less- to “Tarzan and his fucking mother are looking for a flat in Alcobendas” (Alcobendas is a “dormitory town” near Madrid)
(Well, the translation of the name is not literal – It would be “Tarzan and his whore of a mother”, but the “cultural” translation here would be “his fucking mother”).
Used to be a San Francisco band called “Shitty Shitty Band Band”. I know nothing else about them, but their name still makes me laugh.
My hub and I used to produce bands at local pubs. Sometimes we would have cancellations and have to get whatever local band we could to open, even if they didn’t mesh with the style of the headliner. (Without an opening act small touring bands are mostly going to have a zero audience) A lot of the band names were particularly gross or offensive. We had one all female lesbian band from Northern Alberta get very upset about having a band called the Vagina Wizards opening for them. That was one band that didn’t opt to stay at our place the night after the gig; I think my husband pissed them off.
What other band names do I know of? We never produced them but the Greasy Creases just sounds particularly vulgar to me.
I’m guessing that that is a riff on Nitty Gritty Dirt Band…
Or “Chitty Chitty Bang Bang.”
Pussy Riot is another one that the media had a field day with, trying to say/not say it, when they were on trial.
You missed Sweaty Nipples? Aww.
Otoh, I always found the name “Cherry Poppin’ Daddies” *really *offensive.
Hey, My band opened for Sweaty Nipples in a NJ club in the '90s! I remember them having this driving percussive sound that I found infectious (in a good way) and they used samples in a cool way. Kind of like Faith No More or Nine inch nails but with more percussion. Head Like a Hole but a little gentler. They were touring in this beat-up converted delivery van-looking thing fitted out with bunk beds. From Oregon. I thought it was pretty hard core.
My favorite band name from days of yore was Screaming Headless Torsos
Just having a quick look through some Gothabilly bands and I’ve found Cult Of The Psychic Fetus, The Gettin’ Headstones, Dante And The Infernos, and The Cryptkeeper Five.
Gothabilly is a bit silly.
Here in the land of Oz we have band called The Beards. Because every song they do - every single one - is about beards. My favourite is “If Your Dad Doesn’t Have a Beard, You’ve Got Two Mums”, although “You Should Consider Having Sex With a Bearded Man” comes close.
Back in the heyday of punk we had “The Snivelling Shits” which I liked (the name of) a lot.
My buddy John put together a band for another friend’s wedding. The didn’t write songs, they played covers. Covers of songs by one artist. Covers that John arranged by listening to Neil Diamond albums non-stop for like 4 months. Oh, and he arranged them all as hardcore punk rock tunes. Did I mention that he plays multiple instruments and has no formal musical training?
Anyway, the important thing is that they were so good that we all urged John to book some real gigs, which he did, and we all laughed ourselves silly at the name he finally chose for the band (and how cool it was to see it on a bar’s marquee):
The Giving Heads
Wasn’t there a band called Huge Pile of Dead Jews? I vaguely remember seeing an album cover, but alas, a Google search just turns up CT websites.
“60 Minutes” recently rebroadcast the piece they did on them a while back, and I wondered how many of those words really needed to be bleeped. :smack: I had the same thought after the Chelyabinsk meteorite, and sure enough, PBS addressed this when NOVA did a show about it a few weeks later. It was weird hearing people say things that were gibberish to me, and hearing lots and lots of bleeps. 
BTW, I remember when the Butthole Surfers had a hit single. I would have loved to hear Casey Kasem say THAT name!
And many years ago, I dated a man who owned a used record store, and he once got an LP by a band called Scraping Foetus Off The Wheel. It was purchased by his partner, and he wondered who could possibly want to buy it (neither of us knew what the band actually sounded like) and one day when I was in there, someone came in LOOKING for it! My XBF said, “What do they do, run over abortion clinic rejects?”
It’s just one of JG Thirwell’s personae. See also You’ve got Foetus on Your Breath, Clint Ruin etc. He used to collaborate under various guises with the likes of Lydia Lunch, Nick Cave, Sonic Youth and that sort of arty crowd.