Nerf Herder
The Presidents of the United States of America
Two bands who, not only do I think they have cool names, I like their music, too.
This is exactly the type of post I was trying to discourage.
mmm
I was going to mention Steely Dan, but someone already mentioned that, so I’ll go with:
Led Zeppelin
Nine Inch Nails
Queensryche
Smashing Pumpkins
A Perfect Circle.
The Dead Milkmen
The Crucifucks
The Dayglo Abortions
And I am a fan of each. 
Here’s my top ten favorite names that I don’t think anyone’s listed yet. No particular order:
Supreme Beings of Leisure
Guns & Roses
Black Sabbath
Blood Sweat & Tears
Tower of Power
Cowboy Junkies
Creedence Clearwater Revival
Velvet Underground
Styx
Tangerine Dream
Dayglo Abortions.
Also I know we’re talking about bands, so while I’m mentioning Impotent Sea Snakes, what I really want to note is their lead singer is named Buck Futt.
It might be a stage name.
The Mothers of Invention
Spyrogyra (jazz band)
1000 home dj’s
I like bands with literary allusions behind their names. Like the Doors (Blake via Huxley), Veruca Salt (Dahl), Uriah Heep (Dickens), and Modest Mouse (Wolfe). I don’t know if Aerosmith even knows Sinclair Lewis wrote a book by that name though (spelled differently). There are lots more.
Blood, Sweat & Tears
Harvey Danger
ETA:
The Flaming Lips
The New Pornographers
The Wallflowers
Semisonic
Fastball
Imagine Dragons
Of Monsters and Men
Cage the Elephant
Fall Out Boy
Fitz and the Tantrums
Nathaniel Rateliff and the Night Sweats
Walk the Moon
Moon Taxi
Thirty Seconds to Mars
Panic! at the Disco
Lovelytheband
Head and the Heart
Kings of Leon
NWA, says it all really!
Ones I like:
Belle and Sebastian
Southern Death Cult
New Order
The The
Einstürzende Neubauten
Prefab Sprout
The Fall
Dead Can Dance
Alice In Chains
Talking Heads
XTC
X
The Ex
Them
The Herd
Human League
I think The Beatles qualify on their own:
A. Get it The BEATles.
B. Homage to Buddy Holly and the Crickets.
Cool band name, bro.
Garfunkel and Oates
When People Were Shorter And Lived Near The Water (yes, they have a Wikipedia page)
Eagles Of Death Metal
Twisted Sister
The Bad Plus
The Alan Parsons Project
Badly Drawn Boy
Jehova Waitresses
Jon Cougar Concentration Camp
Metallica