How about  Camper Van Beethoven

Redneck and The Red Rectums (saw them in northern Minnesota (around Ely)).
 
Edit: around 1967

Not that long ago I was looking for a band name to call myself. I tried every weird combination I could think of, then googled that name....And every one was taken! In desperation, I tried one that I thought no one would EVER use:
"Severe Tire Damage". Guess what? Yep, there is a band called just that!
 
There is actually at least one web site with an app that will automatically generate band names for you by just tossing together random words. Some of the names are actually not all that bad.
 
I have determined that a good way to get a not-too-bizarre unique band name these days is to use a person's or pseudo-person's name. E.G. "Billy Joel", "Jethro Tull", "Pink Floyd" etc..