The stars are all taken for real data. Is it complete? Probably not. Some star system names may not match the catalogs you look at. There are stars with multiple name references, how the devs decided on these names, I'm not sure. There are Arabic names, also by constellation... such as alpha, beta, gamma.. etc prefixed by the constellation name, and numerous stellar catalog refereces. 2Mass is one such catalog, for example. Stars in an actual constellation can be spread out over vast distances and are not always localized within the same region of space. Constellations are an artificial abstraction as seen from Earth. So this is why one star in Bootis could be 100ly away, while another star could be 300ly away, intermixed with stars not in the constellation. The constellation stars tend to be brighter, thus visible from earth, while the other nearby counterparts may be less luminous..and not have more formal names. The human eye at best can see down to magnitude 6 under a perfect dark sky.. which is not very far distance wise on the galactic scale.
From what I read.. and I may not be entirely correct here: Frontier uses some sort of algorithm based upon known scientific data/theory... and some guesses/interpretation to make it practical for a game. Every system starts with a seed, from which it is procedurally generated. The seed is the star type, the number of stars, their masses, their relative position, and add in a cocktail of physics concepts. The game then makes a 'best guess' at how a certain system 'might' form, assuming said theory is complete. Which it is not. It essentially seeds the system, then evolves it to the current star date of the game. Thus you get planets moving in orbits and position based upon the current date/time. Everything does move.. and consistently.
I hear they may be populating 'known' systems, such as the many hundreds of systems found to have exoplanets in recent years. So besides the seed data mentioned, they have the ability to custom overlay systems with known true to life data. How far they plan to go with this? Who knows. It probably entirely depends on interest and how long the game and development can remain supported (profitable).
I am quite impressed with what they have done! FYI, some background. I studied cosmology (astro/physics) at university. Though I don't work in the field I'm an avid hobbiest. I observe and do astro-photography, and this stuff perks my ears up every time!
Elite gives a great human understandable view of how vast our galaxy is, and how many stars are really out there. Still think we are alone? Our galaxy is only average. Smaller than average for the most part.. and there are estimated to be about 100-200 billion other galaxies of all shapes and sizes out there in the known universe. Many far far larger than our own.