Hein is a unique character only from FFIII that has a unique story. Having him appear on XIV with the same name AND appearance would imply some sort of cameo/dimensional rift sort of like Dissidia.

Amon, on the other hand is a name given to the clone mob with no back story, and thus the name Amon can be used without implications and can receive a back story as a character for a different FF game. You already mentioned the Crystal Tower motif.

So, I think Yoshi P had him named Amon instead of Hein on purpose and that his reasoning essentially was that Hein is an existing unique character in another title already and he only wants the boss type with a new character in XIV.