The name 'endless desert' has nothing to do with its size. Rather, people originally had no way to cross it, or escape it once they were inside, so it was called the Endless Desert because people didn't know any better at the time. The name stuck although crossing it is now more than possible. The sands of the desert are primarily owned by the Crescent, the largest functional Empire on this side of the world, however there are plenty of places within the sands that are outside of their purview.