Technically, the map should be rotated 90 degrees anti-clockwise and then it would be correct.
However, fuck you, I am not doing that. This is accurately enough.
Anyway, here are a few basic names. Feel free to give them your own, excluding Tzeentch's Rhombus.
I mean, even on the original map, I unintentionally put four absolutely fucking TERRIYING systems in an almost perfect parallelogram.
You've got your frontier space - it's not anywhere near the Halo Stars, really, but it's on the very, very, very of that spiral arm, where there's almost no stars at all.
Industrial space, only named such because, fuck, look at it. Contain shitloads of mining and industrial and administrative planets. Other than that, it's fairly mundane.
Central Space, because there's where all of the capitals and everything fancy and nice is.
Xenos Space needs another name, only named as such because there are two planets that are very dreadfully Xenos.
Then you've got Heathen's Gaze, only called such because all of the planets in that region are capable of seeing a particularily large warp storm that I am tempted to include on the map. This warp storm is the primary source of all the political unrest in the area and most of the heresy. Needs a decent renaming.
Also, ruined space, a rather non-descript area of land that well... fuck, nothing special about it exept for a third of them being dead planets.
All needs a bit of renaming.