The idea that they'd make him a different person altogether strikes me as completely bizarre. If they were going to do that, why even call him Khan in the first place? What would be the point? Okay, maybe "Noonien Singh" adopted the first name Khan at some point in life -- it would make sense if it were an affectation, since it's rarely used as a given name -- but of course it's supposed to be the same person.
Although, on a related note, IDW does acknowledge the difference in appearances in the MU story. At the beginning (set in the regular Abramsverse) Scotty and Dr McCoy are discussing alternate universes, they are shadowed by their Prime Universe counterparts, drawn in the likeness of Doohan and Kelley. I've actually come up with my own theory (as a joke, not a serious suggestion) that there's something in Vulcan and Romulan biology that when see someone in different universe they can recognize them, but someone of a different species can not. Explaining why Spock can recognize Kirk and Scotty and Nero can recognize Kirk. But were a human or other race from the Prime Universe were to visit the Abramsverse, they wouldn't recognize anyone.
The reason that I am bothered by the change in Kahn and not the other characters is because it is such a drastic change compare to the others. Most of the rest of the existing cast is similar looking enough that I could buy that they are the same person, but Kahn is way to drastic of a change to be able to just blow it off. I don't need an explanation, but I'm not mad we do appear to be getting one.
I take that as artistic license -- or simply as a bad idea. It's worth keeping in mind that the comics aren't canonical, and however much they may claim to be keeping the comics perfectly consistent with the films, they're a secondhand interpretation of what the filmmakers have in mind and they contain a number of discrepancies and mistakes. So what's in the comics is not authoritative.
Actually when comparing pictures of Montalban and Cumberbatch there is a considerable resemblance, more so then say between Shatner and Pine.