In Neil Gaiman's Death - The High Host of Living, at the end when Death returns back from her mortal form, we see someone was waiting for her; who was this person she was talking to?
It's Death herself.
Here's the full panel:
As a part of her duties, once a century Death has to take a mortal form and live a day among living things. I interpreted Didi as a temporary Avatar for Death. In the same way as
spoilers from the ending of The Sandman series!
Daniel Hall became the next Dream,
Didi became Death. But also remained Didi. She is both Death, and Didi.