I did not need an explanation for why Klingons didn't look the same in the 1960s vs. every other appearance until Enterprise provided one (though I liked those episodes and have no objection to the explanation).
The same applies to Khan. No need to explain, but as one is being offered, I am interested in how they will try to explain it.
If it were up to me, I would play with the word Khan. In Trek, it appears as much a title as a name (a dual purpose for the term that exists in the real world). Cumberbatch could easily be using "Khan" the way Montalban did in Space Seed (if I recall the dialogue correctly enough from Space Seed to paraphrase, Kirk presses Khan with something like "Khan, just that, nothing else?" to which Khan replies something like "just Khan").
What if Khan is a title and not a name? So far, only Montalban and the 20th century youth have acknowledged or used "Noonien" (Singh would thus be implied). Cumberbatch did not indicate "Noonien" as part of his name. The way 1967 Khan avoided "Noonien Singh", one would think the more famous portion of his identity was his name rather than his title (if "Khan" is indeed a title here).
It is extremely unlikely the writers will go this route (Khan as title), and I have no issue with Cumberbatch being the same in-universe Khan as Montalban. But that is how I would have approached the matter--in large part to add a bit of mystery to the story. Then again, I'm not a screenwriter.