I just don't think that the King's Wit is near as central a role as the PM. Kaladin didn't even know what the role was when he first met Hoid.
So unless knowledge of the role suddenly became far more widespread, I don't think we can say that people on other planets or even other nations know of that title. Wit does continue to use that as his name on Roshar, but he doesn't really act in that role after WoK. As I see it, the reference that he makes to his wit being a part of his sense of self seems to be just a joke for himself.
Of course, I could be wrong and his exploits on Roshar while going by Wit could have made the term widely known. But I just feel that it's gonna be fairly localized and known only by scholars of the Cosmere and Alethi.
This is very true. I was expecting Design to show up once Hoid's curse was broken, but we didn't even get a mention. I don't really know the mechanics of Riina's curse, but could it have affected Hoid's Spirit Web? And if so, could that have weakened, or worse, broken the bond? I think there are plenty of reasons to doubt that (but I think we can't talk about them as they're spoilers for other Secret Projects), but the fact that Design got no mentions at all is a little concerning.