I think it probably isn't Dyme, or any name that starts with 'D'. All of the other Nobodies had a different starting letter from their original name. For instance, Isa and Saix, from 'I' to 'S'. Lea and Axel, from 'L' to 'A'. All of the other members (whose original names are known) follow this pattern.However, this may be just a coincidence, so his name may very well start with a 'D'. It just doesn't seem likely to me.
You can only get 24 combinations out of 'D', 'E', 'M', and 'Y'. Out of the ones that didn't start with 'D', these seemed, to me, to be the most promising (or at the very least, possible):
Edym
EdmyEmydEmdyMedyMeydMyde