well if we were going with an acronym, I've been using "FFG SWRPG" for a while now.We could call it:
Narrative Star Wars Roleplaying, NSWR or NSR
Narrative Edition, NE
Narrative Star Wars, NSW
EAFSW could work too (as in Edge Age Force Star Wars)
i think the 3rd one is the better, it's much shorter than the FFGSWRPG but still defines it well.
Same, I think it's what will actually stick, but it's a bit of a mouthful.