Nakamoto Satoshi to my knowledge never wrote his name in Japanese. Hence his last name could be 中本 or 中元. Both legitimate ways to write it. His first name could be 聡, 敏史, 哲史, etc.
Find a list of possible names pronunced Satoshi here:
https://namedic.jp/names/yomi/m/%E3%81%95%E3%81%A8%E3%81%97

If Nakamoto Satoshi himself didn't write his name, then writing it 聡 is based on pure belief. And Chat GPT has only access to the widespread beliefs on Internet as far as I am aware of.