The starmap itself will not be random. It will be a reproduction of local space and that doesn't really change much. Current plans for the map is to include some of the real area within roughly 150LY of Sol, in 3D. According to Google, that's some 21,900 stars within a 150LY radius, so maybe just the spiffier ones...
The Sol System will also be pretty much the same from game to game unless they start demoting a few more planets...
Inner Core systems will have some random smaller features but will have their larger attributes common to each game. Lets face it, when you make a trading game you don't put Genoa on the top of Africa or anything. The main inner worlds are most commonly known in slang as The Big C — Civilization.
Most politically linked worlds are referred to as Arcs usually in reference to the way worlds are often developed one after another down the spiral arm. So there is the Russian Arc, The Chinese Arc and so forth.
When an arc is less of a long group and more of a single line these are referred to as Strings. So you have the American String, the French String, the Canadian String and so forth.
As you head out down the lines and into the Scatter, then the system details themselves will be completely random.