If keeping with West End Games tradition, they also tended to refer to the New Republic as its own period. However, this would be more of a Legends reference, not canon. Also, I need to watch the movie again, don't remember if they referred to it as the Republic or New Republic. Any who, for canon eras you could also have a phrase to refer to the period between the Battle of Endor (or Battle of Jakku?) and when the First Order made their first strike against the Republic with Starkiller Base. Perhaps "Post Empire"?

Afterthought for that previous comment: making a term for that specific time period wouldn't matter much unless Disney/Lucas Film/(who's in charge now?) begin publishing stories that fill in that era, and if it's significantly different from the Empire and First Order eras.

I completely agree, the New Republic and New Jedi Order Era's exist on the site, and I don't see any reason for messing with them.

As for the Post Empire era, I agree with your second comment, lets deal with that problem when we come to it :D