I think the distinction I would draw is between the time when pretty much all band names were collective nouns–The Whoevers–and when they no longer had to be. They could be singular nouns, proper or otherwise (Pink Floyd, Jethro Tull, Jefferson Airplane, Canned Heat, The Who, The The, Poison, Earth Wind and Fire) or, eventually, not even nouns (And You Will Know Us By the Trail of the Dead, They Might Be Giants, The Moon Lay Hidden Beneath a Cloud, [In]Sync, Take That, OK Go, Yes, Wham, Aha, No Doubt, Life Without Buildings, Can, etc.).
For me, the whole “band name!” thing is an exercise in taking a phrase completely out of context and imagining it on its own, as a purely aural artifact, divorced entirely from its original meaning. Some phrases that I’ve come across, embedded in perfectly reasonable context, but that sound "band name"y when removed from context, include Good Quality Frogs, In a Box and Walking . . . and a bunch more I can’t remember at the moment. They’re jotted here and there in journals and, um, receipts and napkins.
Then, of course, there’s the naming tradition that’s older than any of these bands, and continues strongly today: the pun, or other silly wordplay. The Beatles (and the meta-pun take off on The Beatles: The Bangles).The Ink Spots, as mentioned above, while not strictly a pun, is a good example. Das Booty. My favorites in the silly wordplay genre are the celebrity-name mashups: Star of David Brinkley, Elephant Gerald, Rubber DeNiro, Bobbed Illin.
Then there are the literary references: Quiet Riot, Aerosmith, Veruca Salt, etc. etc. etc.
I doubt if it’s possible to compile a complete, organized, categorized catalog of band names, even if there weren’t more of them every day.