The discussion of who is the REAL Pink Floyd, who fired who, who was the brains behind the outfit etc has pretty much been ongoing since 1968 and especially since Waters left/dissolved the group in 1982 (and unsuccessfully sued to stop the others from using the Floyd name). Gilmour is on record as calling Waters a psychopath, if memory serves, and he also likened the one-off Live 8 reunion to sleeping with his ex-wife. In one interview I read a few years ago, keyboardist Rick Wright claimed he was still in therapy to deal with all the conflicts within the band (specifically his being sacked during the recording of The Wall; he played on the tour as a hired session musician - not a bad idea in retrospect since the tour actually LOST money...)
Fun fact: the last time Floyd toured (in... what, 92, 93?) Waters supposedly tried to sue to stop them. They had the rights to the songs, but they did NOT have the rights to the famous flying pig that's supposed to soar over the crowd. So Gilmour simply had a new pig made - of the opposite sex to the old pig. If you look at the Pulse live DVD from that tour and wait for the end of the credits, there's a line that says "Original pig concept: R. Waters". That's as much of credit as Gilmour is willing to give him.
Personally I think Waters' solo albums are at least as good as the two rather tepid studio albums Floyd have put out since 82. At this point, they haven't released an album in almost 15 years and I think the only thing stopping them from officially calling it quits is that Gilmour doesn't want Waters to be able to tour under the name...
Going to see Roger Waters perform Dark Side of the Moon in its entirety in a few weeks. It's not going to be quite the same thing, but as close as you get these days I guess.
I never knew how they picked their name, interesting blending of two guys they respected.