Chapter 1

All mortal minds shook, ever slightly, at the Endless Dream's passing. But Dream was just that, Endless. It would be a paradox if that which is Endless, truly ended. Therefore the old consciousness of Dream faded into backlogs, so a new Dream could be born.

It was Death that the new Dream met first because, like with any good story, the New Dream's life started with his death.

Alternatively: Morpheus croaks and a 17-year-old becomes the new personification of dreams. At least he'll get a new loving and supporting family... kind of.