Take any phrase/object and put "The" in front of it.
I figured that out when all of those retarded band names were coming out like The Shins, The Killers etc.
Aww, you killed the thread now usedtabe, by technically posting every possible name for an indie band in one fell swoop.
Little Johnny Emo and the Menstruating Elephants
Fisto McGee vs. the Corrupto-meter
I'm better at metal names, probably
Tugamuffin and the Monkey Men
Two Ton Toenail
Insert Independent Musical Band Name Here
Also, I'm bringin' back the Pen Cap Explosion?! one last time! Suck on that people who may or may not enjoy the act of drawing succulently upon extra-bodily objects!
Suction Biters of the Danish Apocalypse
Indie bands love upper class or nautical terminology (Beach House, YACHT, etc.) so you have your choice, really:
Courtesy Of Wikipedia, using only the letter "A" and with the liberal addition of a "The":
The Absolute Bearing
The Anchor Home
The Anchor Sentinel
Arc Of Visibility
The Aye Aye (or maybe The Aye Aye Aye?)
The Azimuth Circle
Casual Awkward Conversation
Look, Mom, I'm Sad
This Band Used To Be Cool
The Legend Of Meh
Hibbity Skibbity Bop
and my favorite...the name of my indie rap group...