This has bugged me for a long time.
But after hours of thinking, I think I understand it:
Heartless are the embodiment of darkness in the heart of someone. With pure-blood heartless, the darkness grow and consume the heart that goes to the depth of darkness. What remains is the heartless. I don't think pure-blood heartless steal hearts. However, emblems heartless do. They are artificially created and therefore do not need to consume the heart of their victims. They just attack and steal them to multiply. So the name is a bit misleading.
Nobodies are more to be taken as "nobody/no identity" rather than "no-body".