There’s a pretty terrible Auckland punk band called Girls Pissing On Girls Pissing. Not hugely offensive per se, but I always get a kick out of imagining people saying they’re going to see them live.
Shirley Temple’s Pussy, who changed their name to Stone Temple Pilots.
I had the pleasure of seeing ‘Kunt and the Gang’, a couple of times, about ten years ago. Some good, obscene comedy songs. But it was also funny how there was no ‘Gang’. Just Kunt by himself, playing juvenile songs about masturbation, fittingly.
Not really offensive I guess, but it was startling way back when they were around:
Root Boy Slim and the Sex Change Band and their best song, “Boogie Till You Puke”.
Dennis
They weren’t around when this thread started but I have every recording that I know of from Austria’s Vaginal Penetration of an Amelus with a Musty Carrot, including the split disc they did with Teen Pussy Fuckers.
In its time, The Fugs was pretty obscene.
The Mothers was considered too dirty by their record Company, so they added “of Invention” to their name.
I love the Butthole Surfers, but I’m guessing they never would have had a hit if they’d kept one of their original names, The Inalienable Right To Eat Fred Astaire’s Asshole.
Then we also have:
The Scrotum Poles
Bogshed
The Angel Sluts
Jon Cougar Concentration Camp
The Slits
Gay Witch Abortion
Joy Division
Cuntz
The Jackofficers (Butthole Surfers side project)
The Brian Jonestown Massacre
The Coathangers
Daisy Chainsaw
Fuck Buttons
Holy Fuck
The Homosexuals
Jackie-O-Motherfucker
James Dean Driving Experience
Johnny and the Self Abusers
King Kong Ding Dong
The Klitz
The Muffs
The Penetrators
Perfect Pussy
The Nipple Erectors
Psychedelic Horseshit
Sex Church
The Slugfuckers
The Snivelling Shits
Sperm Wails
Starfucker
Slutever
The Urinals
And one of my favorites, Tragic Mulatto, which is not too terribly offensive, but they did have an album called Hot Man Pussy, and their lead singer named herself Flatula Lee Roth, played the tuba, and usually performed in a diaper and duct tape.
How about Infant Annihilator and their great song Cuntcrusher…?
There was a local (to me) band back in 1980 or so called Teenage Jesus and the Jerks. Some semi-big names were involved – James Chance and Lydia Lunch come to mind.
Also, an early hardcore band (if I remember right) called Ism. Not so bad, but the frontman went by the name of Jism.
Anyone mention 1000 Homo DJ’s?
Millons of Dead Cops(MDC) might qualify.
According to STP’s Wikipedia page, they were looking for a band name with the initials STP. They thought of that one, but chose Stone Temple Pilots.
For years I thought the name was * Revolving* Cocks, which conjures up quite a different mental image.
GWAR had a member who called himself Jizmak the Gusher, and there was a hair band performer who called himself Jizzy Pearl. niiiiiiiice.
I remember -ism. (The hyphen was part of the name.) There was an alt-rock program on our local college channel that sometimes played them. TJ&TJ was best known for their name.
While I’m on the topic of extra punctuation marks in band names, about 20 years ago, there was a band in my area called Odlid! (Yes, the exclamation point was part of the band’s name.) If you don’t get it, spell the band’s name backwards. :o Anyway, what’s really weird about THIS band is that some Midwestern Walmarts sold their album - while banning a Goo Goo Dolls album because the cover featured a toddler covered in blackberry jelly, which some people mistook for dried blood. 
Huh - a little late to the trough.
Of the seven bands I was in, my first one - Our Testicles Touch the Ground - was probably my most eye-brow-cocking name, I spose. Repulverizer was the most metal-sounding one.
So - because I could easily double all the bandnames mentioned in this thread in both quantity and fucking disgustingness, I’ll leave just a smidge of some of the less nastier ones.
Asspatula
Rapeman (actually one of my favourite bands from the 80s - name taken from a Japanese comic)
Splatterea
Nice View (seriously - DO NOT INQUIRE)
Scraping Foetus Off the Wheel
Dismal Marsh Gas
Fallopian Breakdance
Crazy Fucked Up Daily Life
Rectal Smegma
Intestinal Loudness
Jump Back Jesus
Eggs
Putrid Offal (fun to say!)
Assuck
…some were mentioned here already, but just all the goregrind bands out there, alone, could take up a couple pages here.
::slyly smiles over left shoulder at AxCx tat::
Prostitute Disfigurement is the one that always comes to mind when this subject comes up. But really, there’s so many death/grind bands with that sort of name that it’s hardly shocking these days.
Fun fact: Jizmac is still in Gwar.
Funner fact, my old handle way back in hotail and war craft days was Col. Jizmac.
Well, since it’s kind of devolved in to a lovely collection of offensive band names (and some of my favorite bands), I’m gonna add one of my favorites. But it’s pretty mild. Ancient Chinese Penis was a band from an eon ago. The name’s more humorous if you realize it’s a riff on an ancient (even at the time) Calgon commercial
ETA: And wow, almost nothing but strange penis-related suggestions next to that video.
The “who cares what the band sounds like - did you hear their name?” award goes to My Penis Is Made Of Dogshit.
I’ll contribute The Bloody Stools.