Here's the best you're gonna get. From Wookieepedia:
So far, no serious attempt has been made to give the galaxy an official or astronomical name. According to The Essential Atlas, the Nagai of Firefist refer to the main galaxy as "Skyriver" which it is the closest any official material has come to naming the Star Wars galaxy. We don't know however whether or how the galactic community name or refer to their own home galaxy (the way we refer to our galaxy as the "Milky Way").