if he were to lose any rights over it, people would soon start naming it under something different
What? You can't be serious. With the trademark/copyright Rubik himself *forbids* other people to use his name. If it weren't for the trademark/copyright, *more* producers could call their cubes "Rubik". You don't make sense.
I am thinking on a long term scale, not in the next couple of years. Ok so maybe Rubik himself doesn't want it to have his name, but, if it is as you mention, and people do want to use his name, then it's clear that people today feel the same way that I do in that it should keep his name.
But in 100 years, when the cube craze has been dead for a long time, and some child finds it in his long dead grandpa's old toy box, and asks his parents, "what's this?" are the parents going to respond, "that's a Rubik's cube!", or will it be something more like "Oh I think that's one of those brain cubes", or whatever.
I think, even if people can't literally call it a Rubik's cube, they should still go out of their way to make sure it doesn't start being called something different that will stick. Rubik will die eventually, and when that happens he will not have any more influence over what happens with his cube, and from then on I think it should be that the name is used on all cubes.
This is not saying that I think Rubik is being rude and selfish with the current rights, but for the sake of history, some things must be done against the inventors will...