So Are We Gonna Start Naming the 'STAR TREK'-Universes by the ''Kirk''s who inhabit them?

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I watched the tenth (last?) episode of the first 'season' of STAR TREK: STRANGE NEW WORLDS ... For one thing, I'm noticing why a bunch of the reviewers make sure to watch 'every episode that's available' before they start a review---it's sort of "embarrassing" to 'guess what's gonna happen' when you could always just "watch the following episodes & SEE what happens.' (I don't think I mean 'embarrassing' ... I mean it's "not the way it was before (when you could see the latest episode & still have a week or so before anyone knows what's gonna happen).") I hope that's enough room for a SPOILER-WARNING (in case you have Paramount+ and want to find out what happens for yourself ... all across the STAR-TREK 'multicosm'). It started back in the 60s (I think) with STAR TREK, when we meet the 'William Shatner'-Captain Kirk. In the run of his series of ENTERPRISE-adventures, we meet Pike---a former Captain of the ENTERPRISE who's now a paraplegic who can only communicate "yes" or "no" through the machine that's also his wheelchair. (skipping over the 'Chris Pine'-Captain Kirk for a second). In STAR TREK: STRANGE NEW WORLDS we meet Captain Pike, who is called to captain the ENTERPRISE after he tried to retire (following some mental trauma that I think happened in STAR TREK: DISCOVERY---which I'm going to watch soon). The mental trauma showed Pike his future---how he was going to END UP a paraplegic because he would try to rescue some cadets from a big explosion. When he tries to avoid the disaster by telling the cadets NOT to join Starfleet, he is stopped by 'himself from the future'---who uses a time-stone to show him what will happen if he sends those letters. I won't tell you 'the reason-why Pike came back from the future,' but--if he had sent the letters--he wouldn't have become paraplegic and would still be captaining the ENTERPRISE instead of the man who would instead be Captain of another ship---the 'Paul Wesley'-Captain Kirk. That's where I get confused because of the 'Chris Pine'-Captain Kirk. In HIS universe (known as "the Kelvin universe" because of the event that created it), Kirk is a 20-something farm-boy whom Admiral Pike (not paraplegic) recruits after a bar-fight! Did the Kelvin-event (where a time-traveling Romulan-radical destroyed the USS KELVIN with Kirk's father aboard (just after Kirk's birth)) incidentally save Captain Pike from the explosion AND get him promoted to Admiral?