Besides, for all we know Admiral Marcus and Section 31 had Khan submit to a form of cosmetic surgery to mask his appearance, which might have given away his true historical identity to somebody along the way. When awakened from his cryogenic canister he looked like Montalban in "Space Seed" but Marcus and others didn't want to take chances that somebody in Starfleet or elsewhere on Earth would recognize that a 300-year-old former genetic tyrant and war criminal was roaming around the 23rd century. So they had him go under the scalpel and....there you have it. Montalban becomes Cumberbatch.
Who knows, really. All we can do is speculate and come up with our own theories because I don't think even the novelization of the new film explains what happened after the Botany Bay
was located other than Khan alone was revived and the other Augments were left in cryofreeze.