Some of the systems reflect real stars, being in roughly the right place, roughly the right type, approximately the right size, etc. Some of them are named, I think, on the basis of requests from early backers - I seem to recall station, NPC and body naming was a backer perk at certain levels during the Kickstarter. And some of them are algorithmic as in the original Elite 1984, where there were 8x255 stars with algorithmically generated names.
I forget exactly how Frontier: Elite 2 and First Encounters did it, but I know Pioneer - the unofficial, open-source First Encounters remake - generates actual names for every system rather than using ED's horrendous STRI-NG0-FG-AR-8A G-3 'system' for naming stars.