Ethnicity has very little to do with geography in modern times, and vice versa. People of all colors, shapes, sizes, etc. come from everywhere with all kinds of different names. Requiring Khan to be a brown skinned man with a certain accent just because he's from a certain part of the world is just a little bit ... what's the word I'm looking for here? ... oh, yeah. Racist.
And maybe, just maybe, Harrison is not really Khan after all. Maybe he's doing a "Dread Pirate Roberts" on their ass. Gnaw on that
for a while.