It's amusing that people are still speculating online it's Khan. I just don't see it and with the recent interviews with Cumberbatch, I think it's safe to rule that out. http://www.bleedingcool.com/2012/12/12/benedict-cumberbatch-talks-about-his-trek-villain-promises-hes-not-khan-under-an-alias/
So who is John Harrison? Well he's not the redshirt from the original series that shared the last name. It's been confirmed that the character has superhuman levels of strength and intelligence. It's here and playing into fan's expectations that I am going to double down on my theory that he's one of the genetically altered super-humans like Kahn was, just not the same man. Harrison will either turn out to be one of Khan's men or perhaps even more interesting the leader of a warring faction from the Eugenics Wars. We know that other warlords existed and fought against Kahn, so it wouldn't be too much of a leap to believe that some of them might have survived and been placed in extended cryogenic sleep too.