1505 stars from memory in those two shots (although it could have been set to 1000). It was supposed to be 2000, but the name lists weren't long enough, and I don't have a fallback name generator yet to add extra names beyond the initial ones, and the game wont allow duplicate names to generate.
The star names are a small list of real names, and a larger list stolen, yes, from Stellaris.
I'll replace that list with either generated names, or suggested names eventually.
Damocles, today if I get a chance, I will be adding in clustering to the disc galaxy generation, so that we get hyperlanes that form space islands of sorts. It'll help give hyperlanes less ability to just go everywhere.
The cluster generation you suggested below, is however, a very good idea for a future generation method.
I have disc already, and will be adding in spirals and rings later.
Some minor alterations to disc generation, and now we have space islands, where exits from the islands (red links) are rarer than links between systems in the island.
The colors on the minimap top left are the islands themselves.
Added an early pass to clusters in. I'll need to more carefully balance their locations. (currently they are pretty random) but it looks like it could be a valid map mode.