That's the tough part. People overwhelmingly just search for the site they want and go to it that way so it's hard to figure out what would take its place other than some form of search. But a lot of people seem to be thinking about this (I remember Google announcing a while ago that they were looking at how DNS could be replaced).

I don't know what a good answer is. From the user perspective it'll likely look more like a search. but technically? Honestly it could remain DNS just abstract away from the TLDs to make them not mean as much.

At least that's my opinion.