I think the Foggerty BROTHERS took a heated difference to the death bed. I also look at the ego driven gripe fest between members of KISS. EEEEVERYONE wanted the ORIGINAL guys. I believe I heard their differences showed its head with the R&R HOF. As far as names of Bands carrying on goes. If I'M a founding member, I'd be all for it carrying on as long as the fans still care.
Though I do not follow U2 like I did 30 years ago, I have heard that the four of them allow input from ALL members. Even Drummer, Larry Mullen Jr and Bass, Adam Clayton....men of very few words, have all the say that Bono and The Edge do. Something that pissed me off with Henley and especially Frey of The Eagles (They are A Holes in my book) U2....They are in each other's hair for a while, while they do a record and then tour. BUT, when a tour is done, they go their own way for a bit. They have been a band since 1978 and have never had a rift or member change.
