I'm not happy with anything of the form "[Something]verse." It's too slangy.
Well, you can't say anything like TOSē or anything derived from TOS since the Abrams-controlled franchise hasn't featured a TV series, and you can't just call it by name since there would be confusion with the original Star Trek
, so it kind of limits your options a bit. Calling it a universe or verse is vague enough to fit in any books, comics, or movies yet descriptive enough to acknowledge that it's set in an alternate timeline.
How about something like Trek Reboot Era