dark both is and isn't the kokuyoku (black wings.) he can reclaim his place as a 'complete' work of art and finally put an end to his 'endless' existence, but he doesn't really want to. yes, his 'true' name should technically be 'kokuyoku,' yes, the majority of any non-humans would recognize him as 'kokuyoku,' but in any setting, verse, scenario, etc - he still does not want to be called by his 'original' name. it makes him happier to be called just 'dark,' because he's always so deeply marked by his own stubborn independence.

he chooses for himself, lives for himself, and doesn't ever abide by anyone else's wishes if they conflict with his own desire. he's got a rebellious streak, he's lucifer-coded, and whatever the immutable heavens or unchanging destinies around him might dictate, if he dislikes or disagrees with it, then he has no problem rejecting it to try to pursue his own paths instead.

it's worth mentioning that he's not the very first 'phantom thief dark,' either. even prior to his awakening as an entity (and curse) within the niwa's bloodlines and bodies, daisuke's far, far, far distant ancestor was active as a phantom thief using the pseudonym/call card signature of 'dark' as well. when dark says he can't exist, and could never have existed without the niwas, he means it. they're never just his hosts or marionette-meat-puppets the way krad treats the hikari; for dark, even as the 'other self' of the niwa, it's the niwa who serve as the 'other self' for him.