Absolutely not J.J. Abrams. Assuming there does end up being more than two movies in the rebooted series, naming the tag after the director of the first (and most likely second) movie doesn't really make any sense.
Looking forward, 2009 seems rather obscure as well. In 2015, when the third movie comes out, do people really want to remember what year the first one was?
I don't see much need for any specific tag right now. Remember that tags are all about following distinct sets of questions. Are there really people interested in following questions about the single (at this point, plus pre-production sequel) movie and not any other Trek?
If there is, I would suggest star-trek-reboot.