One that I don’t think you can have… (I like it too much for if I ever play with my guitarist again in public):
Blue Irony
Made with Real Lemons
We were trying to name our church band a while back. We considered all the typical criticisms: too loud, too much drums, etc.
Name we came up with: Negative Feedback. 
How 'bout “The Band Which Will Remain Nameless”? 
I recall back when The National Lampoon was actually funny…there was a list of reportedly genuine band names. Two of my favorites: “Roman Holiday and the Ouchtones”, and “The Clogs of Isis”.
You could use a band name generator. There are three links on this page to generators: http://www.afm.org/public/musicbiz/bandnamegenerator.php
There’s also a page full of links to contra dance and old time bands. You wouldn’t want to copy them but you might get some inspiriation. Two I like are the String Beings and Carnival Knowledge. Anybody who was following Bretton’s thread on Cripple Creek might want to check out the link to the New Pilot Mountaineers at this page.
http://oldtimemusicanddance.homestead.com/
One of my favourite band names is The New Crusty Nostrils. I’m not sure where it came from.
Steve
Five Times the Trouble
Instrumentally Sound
We Play Music Now
Strings&Pipes&Fipples OH My
The Resonant Retirees
The Stringed Fipple Fever and Pipes Quartet Plus One
PhilO
How about Kate and Four Guys with Wind?
ROTFLMAO!
I’d use it in a second, but I’ll bet the committee will never go for it. You’re probably safe. Several of the others are pretty good too. We may be onto something. Thanks a bunch.
MC
How about “The Dreamtown Rovers”
Great idea. We hadn’t thought of using googlisms.
MC
Another great (and endless) resource for random band and/or album titles is the Googlewhack “stack” at http://www.googlewhack.com/tally.pl.
Have fun!
Be seeing you,
eric.
As a physics geek, I’ve always wanted to call a band something like “Doppler Shift” or “The Event Horizon.” Not even remotely celtic, but I still think they’re cool. Which, I guess, says a bit about my level of coolness. Hehehe… 
A.J.
Bunch of keys
Smash the windows
Bag o’ spuds
Bob’s yer uncle
The proddies
The unrighteous brothers
Ulster madness
Calliope House
The jig is up
Nick Whitmer was in a band named The Jig is Up, IIRC.
I like ‘Bob’s Yer Uncle’ a LOT. And since you’re in ol’ Alabam, you could regionalize it thus: "Bob’s Yer’all’s Uncle’. 
cat.
NOTE TO SELVES: If there’s ever a C&F CD, how about ‘The Fippling Chiffs’?
I vote for “Absence of Imagination” 
I always wanted to name one “Ummm and the Uhhhhs.” Hey, seriously: Smash the Windows or Scatter the Mud might not be too bad. Or you could always mix & match tune names – i.e., “Saddle Misfortune” or “Toss The Pony” …
Yeah, I really like it too. Hey, since we’re all from the South, how about “Bob’s Yer Uncle, Yer Brother and Yer Cousin”?
Or you could call yourselves what we call my boss: “Uncle Daddy.”
There are 5 of us (4M 1F), we all play multiple instruments and switch up quite a bit. Collectively we play 2 fiddles, 3 mandolins, 1 tenor banjo, 2 guitars, 4 whistles, 2 low whistles, 1 uilleann pipes, 1 Scottish smallpipes, 3 bodhran, 4 vocal.
Well geez, you didn’t mention that your band members are octupi. That changes everything.
With that many trad instruments switching off, maybe you can call yourselves “The Moving Targets.”
Caj
Oh, dear, I really must go to work now. But good point, Caj! Maybe they should look at the mountain of gear they’re hauling to gigs and seisuns and go from there … i.e., “The Roadies” (“The Roadie-O’s”?) or “The Overflowing Boots” or “Too Much In The Trunk” or “The Bulging Hatchbacks” … Or maybe just “Gear Mountain”?
And then there are my friends who were opening for a band called “Beyond the Pale” so then and there they decided their name should be “The Pale” …
Okay, to work. Oh, one more serious one: “The Last Pint.” Lovely tune, nice name, sort of a UK flair … ???