John Harrison is probably a pseudonym. He could be anybody - not necessarily anyone we met in the prime timeline who's named Harrison.
Me, I think he's either Garth of Izar or Gary Mitchell.
If it is a pseudonym...then why make him Garth or Mitchell in the first place?
You know what I think is curious? Where did this idea that "John Harrison" is a pseudonym come from? I saw no official statement that even hinted at that, so... is there one, or is this just fan speculation? I genuinely want to know.
Supposedly, concept designs of the gattling gun Harrison is seen wielding in the trailer as he fights Klingons refers to it as "April's Gun" beginning a theory that John Harrison is an alias for Robert April. But of course, according to half of fandom, the character has to be Khan, so now we believe it's an alias of Khan. Or Gary Mitchell. "April's Gun" is now believed to mean "gun designed in the month of April."
Was it ever an official statement that the bad guy in ID would be someone we've seen before during TOS?
If so, Harrison could very likely turn out to be a fake name.
Yes, Abrams or Orci or one of those dicks confirmed Cumberbatch is playing a "canon character." Of course since there is a Harrison in TOS that doesn't really clarify anything.