In the beginning, Sato mentioned if The Head of an Ajin was severed from the body and a new one was allowed to grow, a New Person would be born. So why does Sato remember everything he did, also mentioning about phase 2 of the game?
The "New Person" you are referring to is more of an existential idea than a practical issue of memory. Sato threatens that he will cut off the main characters head and show him his body as the body regenerates a new head. When this happens, the stream of consciousness splits in two.
The original head will be alive and witness the existence of the new head. The new head will witness the old head die The new head will remember seeing the old head but not watching the new head form.
The old head will have a stream of consciousness in which it lived, generated new memories after the branching, and then died without that stream of consciousness going somewhere else. Clearly the old head actually permanently died. The fact that the new head has most of the old head's memories is largely irrelevant. The old head died which is the head Sato is talking to and a new head/Person took its place.
Practically, the new person would pretty much be the same person but this is an existentially terrifying idea.
The irony here, of course, is that this happens to Sato at the end giving the viewer a level of satisfaction watching the villain... in some way... dying.