I will go with Kelvin verse. I don't like the name JJverse or Abramsverse because it gives JJ Abrams too much power and dominance over the series, something I will find odd since I heard he was never really into star trek.
I wish people would stop assuming that had any relevance. Harve Bennett and Nicholas Meyer weren't "into"
Star Trek either, but most people loved their movies. This isn't a hobby, where your fondness for a thing is the only relevant parameter. It's a
profession, and what makes something good is the creator's skill. I mean, good grief, it's not like Robert Butler was a
Star Trek fan when he directed "The Cage" in 1964, since nobody could've been yet. But he still did a terrific job at it. A creator's job is not to
be a fan, it's to make something good enough that it turns people
into fans.
Aside from that, I agree that naming a continuity after a single person involved in its creation,
regardless of one's opinion of said creator, is awkward and undesirable. After all, such a creation is a collaborative exercise, and if it's successful, it can live beyond any single creator's involvement. We don't call the Marvel Universe the "Leeverse," even though Stan Lee was pivotal to it, because others like Jack Kirby and Steve Ditko were pivotal too, and because it's continued to thrive under new creators long after Lee retired.
Spock married his surrogate daughter in TOS? Yuck.
I question that interpretation of Spock's relationship to Saavik. It comes mainly from the novel
The Pandora Principle, I think, and there's no indication of it in the films (especially given that they implicitly had sex in
The Search for Spock). He was her mentor, and in the unofficial backstory he was her rescuer, but any presumption of a father-daughter relationship is conjectural. If anything, a number of versions of Saavik's backstory have had her raised by Sarek and Amanda, making her more of a foster sister, though a generation apart so they never would've actually lived together as siblings.