When the Heart moves onwards to become a Heartless, it forgets everything. The Memories, having to go somewhere, remain with the Nobody.
I think all Nobodies have Memories if only because that's what even enables them to have a physical form and shape - how well they remember how they used to be can even get them to be Human-Nobodies.
I doubt the lesser Nobodies can actually recall those Memories, though, and if they can, I doubt they can tell them apart from the rest of reality.