I am in the Alice In Chains camp who loved them from 1990 onward. Gave the new version a fair shake and love what they're doing too. Made peace with the old version being gone forever, and am capable of liking William DuVall just fine, the new studio album was great, and live they're tearing it up. That guy can sing any way you cut the cake.
I would prefer the new Kyuss album to be called Kyuss over Kyuss Lives. And I'd rather it be called Kyuss over a new made-up name. They've earned the right use their own name- even though Josh is not a part of it any longer. He made his bed, and that's fine. It should be fine for everyone else. But even though he was principle songwriter and his guitar tone was key to that band- the bass, drums, and vocals were also key. It was the four of them as a whole that made it what it was. They've had to replace one of the four, therefore to me they can still call it Kyuss, they have earned it. I am looking forward to hearing what they do for the next record, and am really psyched to be catching both the Pomona and San Diego shows coming up...
Problem is, there's no way they can win in this situation. If they have most Kyuss members and go under a new name, people will cry that they're trying to pull a fast one. If they use the name, then people will say they're just money grubbing and appealing to nostalgia. if they use the name of a Kyuss song for the band name, it seems like they're just sad and pathetic and doing the standard reunion shtick that has been done to death by hopeless people with no shame.
Seriously, the best scenario (which would still be bad) is to go under a different name and play a have different sound. Be a different band than Kyuss. But people will complain about that even and say why not just do some new Kyuss style tracks?
They should either do a trio with no guitar (Scott, Brant, John), or get a bunch of people and do some heavy shit with an Orquesta del Desierto flair. "Brass Band Doom" grab Grayceon, Boris and Blood Ceremony, grab some french horn players and do the whole Captain Planet (with our powers combined) shit.