I'm fairly certain that Anderson does co-own the rights to the band name (along with Howe and White), so he could sue the other band and stop them from using the name. but since he's not a douche he lets the two bands co-exist peacefully and they don't sue each other. But once Howe or White dies that will all go out the window.
It's all depending on the order at which they die though. Anderson seems so healthy I wouldn't be surprised if he's the last man standing (if he goes first then this speculation goes out the window). White has already had known health problems so I'd guess that he'll be the next one to go, but they already have a replacement drummer ready to step in. So White's passing wont affect the current iteration of the band much (sad but true). But Howe's passing definitely will.
Howe is older than Rabin so he'll probably die first, leaving Rabin to be the only surviving Yes guitarist and since Yes needs a guitar player they will end up coalescing around Rabin. and Rabin isn't going to join the Davison group since he's so tight with Anderson. And Anderson and Rabin likely will never work with Downes (since neither has before). So if yes is going to continue after Howe's death (which they probably will) the ARW lineup will inevitably become the official band again.
Unless after Howe dies, the official band replaces Howe with some random (or alternately Sherwood moves back to guitar and they get a new bass player). But I don't think they'll be able to get away with pulling that and still bill themselves as the official band (I wouldn't put it past them to try though).
All that boils down to a situation where if Anderson outlives Howe, Anderson & co will inevitably become the official Yes again.