Where do you stand on split bands with the same name?

I absolutely despise that trend. Obviously, money is the issue, as Queensryche is far more likely to sell tickets than Operation Mindcrime. But it gets pretty ridiculous at times, especially when the bands start releasing albums under the contested name. In addition to the ones you mentioned, there have also been various iterations of Ratt, Great White and LA Guns.

Even without a contentious breakup and a battle over the name, there are still several bands that are the original band in name only, sometimes retaining only a single member. Foreigner is pretty much an all new Foreigner cover band with Mick Jones still playing with them (at least for half the set). In the 1980's YES had an entirely different sound with members from various iterations of the group. And of course we all know about the 2000's iteration of Guns & Roses.

But the question then ends up being at what extent having a single member justifies continuing the name, especially if that member is the creative force behind the band. Megadeth IS Dave Mustaine---Iced Earth IS Jon Schafer, and WASP IS Blackie Lawless. Could you say the same thing about GNR and Axl Rose? Or is GNR not really GNR without Slash?
 
OK but in your example there is a flaw, Megadeth has 2 original members still...both Dave's.

My thing is usually who ever has the singer is the one I will see. Anyone can play the music, but the singer is the "voice" of the band...unless you can;t sing anymore like David Lee Roth, Stephen Pearcy, etc