Or are there, for instance, Qward-Dream and Qward-Death who are not the ones we read about in Sandman?
There's a moment in one of the first Sandman storylines where Morpheus meets the Martian Manhunter who recognizes him as an ancient Martian god. Morpheus is surprised to see a surviving Martian, and appears to MM as the deity he was once known as.
The one we see in the Sandman, Morpheus, is only a single aspect, a single Avatar of the true, gestalt entity known as Dream.
This is discussed several times in Sandman, when we see the Dream of cats, as well as Overture, where we see a meeting of countless Dreams in various forms, whether they be cats, plants, robots, etc.
So yes, there is a Qward-Dream, just as there is a Dream for anywhere else in the Universe.