http://en.wikipedia.org/wiki/My_Penis_Is_Made_of_Dogshit
I strongly suspect I don’t want to listen to it. The name makes me LOL anyway.
I went to their site and listened to samples of a couple of songs. Have you ever watched a Slender Man series (e.g. Marble Hornets)? Where whenever Slendy is on screen there’s audio distortion. It sounds exactly like that, except over music.
My favorite in this category is “I Love You but I’ve Chosen Darkness” - never heard 'em, but saw the name in an Austin City Limits schedule. Yours takes the cake though.
Natalie Portman’s Bald Head is a good one.
Anal Cunt wins forever.
I have to say that even though I like their music, The Darkest of the Hillside Thickets has one of the best band names ever. Sure, they stole it from Lovecraft, but still.
There was a hardcore punk band in Tucson in the 80s that became fairly popular, known as U.P.S., which stood for Useless Pieces of Shit. They had a drummer called Dog Shit.
There was another underground band called Fat & Fucked Up. I always thought if they merged, Fat & Fucked Up Useless Pieces of Shit would be the ultimate band name.
I’m partial to “The Bastard Sons Of Johnny Cash” in the bandname stakes. Also experimental metal band “An Autumn For Crippled Children”.
ETA Also “Wolves In The Throne Room”.
Now you’ve pissed off all the Game of Thrones spoilerphobes by giving away the ending.
I’m joking of course. We all know the lions are there to stay.
[QUOTE=cochrane]
{snip} There was another underground band called Fat & Fucked Up. {snip}
[/QUOTE]
Oh, wow! I was beginning to think I dreamt up seeing that band listed in a Los Angeles music mag in the '80s. (I never saw them because I wasn’t into punk.) More info: Hey "hbo"....
Another one was, “Severed Head in a Bag”. Here’s a clip from the film D.U.I titled, “Severed Head In A Bag-Live 1983”. I have no idea if this video is SFW or NSFW, so I’m spoiler-tagging it just in case it’s NSFW. [spoiler]YouTube.
I’m a fan of (the name of) …And You Will Know Us By the Trail of Dead.
There is a band called Fucked Up that’s achieved some success, and publications that have rules against publishing obscenities (especially radio shows) have gone through some gymnastics to convey the band’s name without actually saying/printing it.
I’m still a fan of “Free Beer,” a group that recorded one album in the early 70s. They took the name because they started out playing in bars and, for some reason, it brought in a crowd. 
Dead Kennedys is still my favorite in the “huh that sounds offensive at first, but then you think about it and realize that it’s REALLY offensive” category.
Thatt reminds me of Illegitimate Sons of Jackie O.
There used to be a band called Reverb Motherfuckers, and at the time, my brother was the student director of a college radio station and at least one DJ wanted to play them outside the hours of midnight to 6am. He wouldn’t allow it, even if they called the band “Reverb MFs”.
A while back, KISS and Alice in Chains toured together, which some people thought was a rather strange combination. I didn’t, because I knew that both bands started out with the same name; Gene Simmons described it on Larry King’s radio show (1980s era) as “the four letter word for sex”.
There used to be a band that did have some commercial success called Butterfield 8, and when they started out, their flyers always said “with bass player Mike Mills” and until people found out otherwise, that drew crowds too because people thought they were seeing an R.E.M. side project.
His name IS Mike Mills; he just isn’t THAT one.
Ladies & Gentlemen, although some (or most (or all)) of these may be NSFW, I give you:
The Fucking Wrath (they sound exactly like you think they’re gonna based on their name)
Gay For Johnny Depp (sadly, this awesome punk rock band broke up last year)
Admiral Sir Cloudesley Shovell
Arsonists Get All The Girls
Atari Teenage Riot
Butthole Surfers
Goblin Cock
Goatwhore
Iwrestledabearonce (awesome band with an awesome name)
As if it wasn’t enough to start a band called Dead Kennedys, now he’s fronting Jello Biafra And The Guantanamo School Of Medicine.
Lightning Swords of Death
The Lord Weird Slough Feg
Stormtroopers Of Death
Uncle Acid & The Deadbeats
1000 Homo DJs
My favourite ridiculous one is “Fuck You Written In Shit”.
Nashville Pussy deserves mention.