In the Prime timeline the TMP-TUC Constitution ships are still called that because they're supposed to be refits of (or based on) the original TOS-era hulls.
In the Kelvin universe that's obviously not the case, as the Ent-A is a separate new class, so it makes no sense whatsoever to also be named Constitution-class.
It's possible that the Kelvin-Constitution class went through another new refit and the Enterprise-A reflects the new version of the Constitution. Or perhaps this is the first refit of the class and the previous refit wasn't a full-fledged class refit and was just some upgrades of the current Constitution. A bit of a stretch since you'd have to accept that Starfleet made one or two major refits of the class in such a short time.
You could even argue that the upgrades they made to the Enterprise in STID were Enterprise-only upgrades, and was a testbed for what would be the full refit of the class, and when the ship was destroyed the next movie, they just made the new ship based on the new refit design.