Khan and Singh are the two most common surnames in South Asia, if I'm not mistaken.
Well, there's the obvious fact that both Khan and Singh can't be his surname in that order.
There have been a couple of different takes on how his name should be "translated":
The assumption back during TNG was that Khan was his "rank" and that his name was Noonien Singh (from which we got Noonien Soong). This has the advantage of being appropriate to at least some Indian cultures, though Singh as the middle name is also common.
SNW appears to suggest that Khan was his given name and his surname is Noonien-Singh which would be very odd, but not impossible if he's "mixed race".