I think it should be taken into account that many of these characters are "in name only", as not to simply rehash the exact same character traits of the TOS crew. Many of them all grow and change in different ways, have different companions, altered back stories, whatever; completely different universe with entirely different possibilities. Having Khan change ethnicity on top of character traits really doesn't phase me, nor does it surprise me.
He could've been Japanese or African, the point is that he was the commander of the Botany Bay, a conquerer from the Eugenics War, and the only, and most vicious of the augmented humans to be taken out of cryo (which, if I can recall, was specifically because he was the commander). Khan is just the name to be associated with that role, so character traits and ethnicity really don't make much of a difference on top of that.
And besides, wasn't there something about identity alteration, name being part of this, going on in Into Darkness?