This has been on my mind for a bit and some of the stuff from the comics has been backing it up. It can be argued that Abramsverse Chekov is a totally different person than Prime Chekov. He's a different age, is physically the most separate from his Prime counterpart, he has very different jobs than Prime Chekov (Ostensibly a TNG-esque Operations Officer, as opposed to Prime's Navigation/Weapons officer.) I also don't recall Chekov being considered a wunderkind in TOS. Granted, we really don't know much about Chekov in the series.
Which is to say that, while he's crafted to be the same as Prime Chekov, stuff they've done to get him on the Enterprise for the films and to give him a job that wouldn't leave him without anything to do, they've essentially grafted an old name onto a new person.