...In essence, Pavel and Pyotr just switched places (that is, names) between the universes.
And yes, any character younger than Kirk could be a completely different individual with a familiar name, "altered" because of Nero's meddling. Uhura, too, appears different: she now is a cunning linguist rather than a switchboard operator, and is romantically interested in Spock - although whether thanks to different body chemistries or just slightly different career histories, we don't know.
Spock's age is somewhat more strongly established than those of the other characters quoted as speculative, because of TAS "Yesteryear" where the only variable is the year in which the episode (stardate 5373, FWIW) took place - a variable in all TOS episodes as well, basically, and not that much of an issue. We learn that Spock was seven years old in a time period that was 30 years in the past of the episode's framing story, sharp. Just a tad older than Kirk, then, and quite in keeping with the various live-action portrayals.