There's no information or details about each star system actually stored anywhere.
It's generated (proceduraly) when the server instance is created at the time you jump in.
The procedure is such that the same system and same planet terrain is generated every time, whether it's already discovered or not.
The Galmap is also proceduraly generated. The procedure generates the same pseudo "random" galaxy and stars for everyone so we all see the same thing.
It would seem from changes that have happened in the past that the star system generation is based on the system name. For example when Beagle point was re-named to Beagle Point, the entire system changed. Frontier fixed it and changed it back to it's original configuration but for a while it was different and we got a clue as to how the system works.
It also seems that system names are based on the Sector name and the x,y,z coordinates within the sector.
Even Frontier doesn't know what's in undiscovered systems since it's all pseudo random and the number of stars is too many to count.
I'm guessing it's a series of hierarchical procedures. First the Galaxy. Star systems are generated based on a Milky Way galaxy model and named according to their sector, sub sector and x,y,z coordinates.
It's not pre-generated, the Galaxy is too big to generate everything. It only generates what you're looking at on the map or where you are.
A star system configuration is based on it's system name and the individual bodies and planet terrain is generated based on the system and body name.
Again, it's not all pre-generated. It only generates it when you're there or looking at a system map.
Or so it seems. This is of course speculation based on what we've seen so far.
There are different systems in the Galaxy with identical names though and those systems are not identical.
This could be because Frontier has a way to re-name systems without changing them (now) or because there's more to the system generation than just the name. The name seems to be part of it, but it's coordinates or other hidden factors could affect the algorithm.
As near as I've been able to figure, Frontier keeps a separate database of discovered systems/bodies and the commander's name that first discovered them.
When you look at a body in a system the game does a lookup and if it finds a match to the body name in the database it shows the commanders name. There is a different database for the Beta servers so you see different first discovered tags in Beta even though the Galaxy is the same.
It can be slow looking up the data because sometimes you can jump into a system and it shows no first discovered tags right away, but after a few seconds, tags can appear.
There are also systems that are not procedurally generated of course. For example the SOL system. These systems are hand crafted and the data that describes them is stored on the servers.