I was never very good at learning covers. In high school, I played in various incarnations of bands, but we tried to do some original stuff. At one of our "shows," however, we did crank out a version of Custom Concern. I have it recorded. In college, as well, we mainly did original stuff.
I can play parts of a various songs: a couple Pink Floyd one's, Led Zepellin, Phish. That's about it.
My high school band covered "God rest ye merry gentlemen," with kind of a punk beat and distorted guitars. My college band did the main theme of Inspector Gadget. Those were probably my favorite covers.
I like the band names idea. When my high school band was going to try out for the talent show, we spent much time coming up with band names. The final two were Optimus Prime and Drownin' Dwayne and the High Water Band. We went with the latter. Eventually my high school band changed its name to Baltimore Jenkins, and my college band was called The Deloris Revenge.
We did plenty of the "drinking band." We played more for ourselves and whoever was hanging around our practice space than true shows.