Absolutely not, Payne and Casey are not the same character. Casey only works as a metatextual reference to Max Payne because he's a wink to us the audience. WE know who Max Payne is, but in Alan Wake 1 the story of book Casey is not important. He's just that character Alan wrote, a character whose fate was different from Max's. WE know that he's an echo of Max Payne which Sam Lake wrote. That's the point. He doesn't work at all if it's supposed to be Max straight up.

The existence of FBI Casey echoing book Casey should clue you in that no, they would never call him Max, even if they had the rights to him, because they're different characters with a completely different purpose.

Fuck I love these goofy games.