He was given a false identity, and as a major historical figure he had a recognizable face. It stands to reason his Caucasian appearance is the result of cosmetic surgery.
It's worth noting that in Space Seed, even Marla McGivers, the historian he hooked up with in that was obsessed with him as a historical figure, didn't recognize him. While it is certainly plausible he had cosmetic surgery to hide, perhaps there is some sort of in universe explanation like his imagine being erased from historical records? Just a thought, because when I recently watched Space Seed I kept thinking how odd it was that no one recognized such a major figure.