It’s a fertile topic:
Sex Pistols (and, by extension, Celibate Rifles)
The Slits
Y-Pants
Hole
Pearl Jam
Revolting Cocks
Anal C*nts
Snatches of Pink
The Dicks
The Hard-Ons
The Genitorturers
…you get the idea.
Hitler’s other nut?
All I can come up with is Citizen Dick…
Oh, does Eric Johnson count?
Third Eye Blind
of course they qualify for being a limp dick band anyhow
The Lovin Spoonful
10CC (if you believe the stories)
Flaming Lips
Butthole Surfers (near the genitals anyway)
LSD-25 wrote:
Cream Corn from the Socket of Davis is one of the most obscene-sounding album titles in history.
If we go there we can include Butt Trumpet.
Talking Heads? 
And also getting close: Steely Dan (dildo)…
Limp Biskit
The band put out an album after David Byrne split called No Talking Just Head 
my favorites…
Nashville Pussy
and
Alabama Thunder Pussy
How is The Lovin Spoonful a genital reference?
It’s a euphemism for semen, like Pearl Jam.
Kate Bush, and Bush 
Captain Beefheart, I heard the name Beefheart came from the discription of his uncle’s helmet.
And allmost every Jazz player’s nickname is a sexual euphemism.
Tool
Arab Strap
The Rolling Stones
Great White
Well, there’s always the Stone Temple Pilots. They’re sort of secretly genital-oriented: before they were the Stone Temple Pilots, they were Shirley Temple’s Pussy.
I thought of a few more:
The Muffs
Snatch and the Poontangs
Mangina
…and, if we’re going there:
Fudge Tunnel
Oh, and:
Doug Clark and the Hot Nuts