flowey doesnt want to be seen as asriel because he wants to keep that last piece of his old life untainted. when everything went wrong, like chara dying, his parents seperating, him dying, thats when asriel ended. asriel represented everything good, so if things weren’t good, he couldn’t exist.

and since flowey isnt good, and the things around him aren’t good, he can’t be asriel. flowey feels different to asriel because he wants to protect his past, protect himself from truly realizing everything he once knew was really gone.