Well, why not?
Bent Wookie
Purple Monkey Dishwasher
Monster Put In Wallet
Some friends of mine had a band called Rex Banner here in Austin. Unfortunately, they broke up about two years ago 
How about:
Taste Like Burning
123 Fake Street
Space Coyote
Rod and Tod
Hell’s Satans
Go, Banana!
That Monkey’s Going to Pay
Flaming Homers
Jebediah Springfield
Guatemalan Insanity Peppers
The ChristPunchers
Kang & Kodos Productions
Hank’s Scorpio
See Montgomery Burn
HellDamnAss Kings
Fighting Hellfish
Homer’s Soul Doughnut
Escalator to Nowhere
I’ve seen a band called Kwyjibo listed in an ad in the local weekly.
The Holy Rollers
The Stereotypes
The King Pins
guess which episode I just saw?
Pressed Peanut Sweepings
Isn’t that the name of Pezpunk’s band?
A friend of mine named his softball team The Hell Damn Farts.
Two groups headed by one man a la George Clinton:
Joey Joe-Joe Junior
and
Shabadoo
also:
Ha Ha!
I don’t have a band name inspired by any Simpsons trivia but I do have a song. The song is called " Cleatus’s Boogie (A Slackjawed Yokels Hoedown)". The tune starts with a rather blistering southern rock sounding riff, goes into a nice shuffle type riff and then turns into a bass based funkfest. Hopefully I’ll be able to get it recorded soon.
Slee
How about Fishbulb?
Mr. Sparkle
Mr. Plow and the Plow Kings
The Bouvier Sisters
Santa’s Little Helper
Sucks Like A Fox
Sacrilicious
Worst. Band. Ever.
Trillion Dollar Bill
Damn Wiener Kids
Egg Soakin’s
No need to make them up, they really exist.
A British (i think) DJ called Disco Stu is known for his song An Englishman in Ibiza, while an indie-pop band from Perth, Australia called Jebediah (named, of course after the beloved town founder) are quite successful on a national level (and have toured the States a couple of times).
There was also a Perth band called Flanders around a few years ago, but they seem to have disappeared, and weren’t ever very successful.
And another Perth band called Cartman is continuing the quest to prove that Western Australians don nothing but watch cartoons.
There’s a hardcore band from Jacksonville, FL called Evergreen Terrace.
Painful Dentistry
How about the Flaming Moes?