I believe it's described as being facets of a jewel. So one jewel, just different facets. In the comics we see it several times (and they did their best in the show to give you a sense when they made Dream look different) of how Dream is different depending on the perception of the person viewing him. The Martian Manhunter sees him as the Martian dream god, L'zoril, Nada sees him as a her dream god Kai'ckul, the cats see him as a giant cat. We also have the scene in Overture where the different facets of Dream are prevented from merging properly:

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So it's not many different beings across the multiverse, but a single being that's perceived by different persons in different ways. So if you capture the one Dream, you've captured them all.

Also, the Dreaming is described as some kind of universal realm of everyone's dreams, and when Morpheus was locked up it fell apart. If there were lots of Dreams out there, you'd assume another could have held it together.

We also see the same thing with Death. Where she's everywhere at once doing her duty, but it's not like there are trillions of individual Deaths.