There are several sources of star system names.
- Original 1984 Elite. Most of these are down around Lave, but there are a few others (such as Isinor) scattered about the Bubble.
- The Elite sequel, Frontier: Elite II (FE2 for short) and its sequel, Frontier: First Encounters (FFE). The FE2/FFE starmap contained some real-world stars (such as Alioth and Achenar) with the rest of the 4,000,000,000 stars (yes, that galaxy was much smaller) procedurally generated. Systems like Cemiess, Anlave and Arexack are "legacy" systems that were procedurally-generated back in FE2/FFE, but have been hand-copied over into ED.
- Star catalogues. A large proportion of the stars wthin the Bubble are taken staight from star catalogues. They have been given HIP and HD catalogue numbers, even if they've been formally renamed.
- ED Procedural generation. There seems to have been a pass-through of a procedural name generator, for the procedurally-generated systems. For example, there's a system named "Bulkuylkana". Not far away from there is another system with a simlar name, "Alkuylkano". Doing a Google search on either of those two words only comes up with references to ED, so those don't appear to be named after some obscure deities or villages somewhere. They sure look like the results of some kind of procedurally-generated nomenclature.
- Kickstarter backers. If you paid £750 or more, you bought the right to name one star system, as well as one planet and one space station within that system. If you paid £3000, you could name two star systems. "George Pantazis" was one of those £3000 backers; his relative Michael got the second star system name.
- FD's own cadre of imaginative cartographers. Systems like "Gurney Slade" are, no doubt, named by someone in FD who loved obscure British 1970s TV comedy shows ("The Strange World of Gurney Slade"). There's also a liberal smattering of systems named after features from ancient Earth mythologies and cultures (eg. Isis, Jotunheim, Vulcan).
- Memorials. Several systems have been renamed as memorials.
- In-game events (usually after colonization CGs). The uninhabited star system HIP 101110 was renamed "New Yembo" after the successful completion of the Yembo colonization CG. LIkewise, several of the newly colonized systems along the Sothis Spur were all given Sirius-themed names after the Sirius Corp colonizastion CG ("Sothis" is the ancient Egyptian name for Sirius).
As you can see, it's an eclectic, complicated and often self-contradictory list.
Now, for your specific situations:
After 1,000 years I imagine that 61 Cygni would become THE Cygni system, or with 5.9 billion of inhabitants, Goombridge 1618 would become THE Goombridge system or been given another name by the virtual population.
Have you heard of the
Macedonian naming dispute? One country in Europe wanted to call itself "Macedonia"; a neighbouring country objected and insisted that the name "Macedonia" belonged to them. The dispute was finally resolved, some thirty years after initiating, by the first country agreeing to call itself "North Macedonia".
I'd imagine a similar situation would happen here. There are two inhabited systems whose names begin with "Groombridge" (number 1618 and number 34). And there must be half a dozen other systems with "Cygni" in the name (such as Epsilon Cygni). So, those systems might be up for a fight if another system tried to "steal their name".
But I do agree with you, that the locals who have lived there for over 1000 years are likely to come up with more original names for their systems, and especially their planets, than what we find in ED. Especially for systems with BD catalogue numbers for names; I've always wondered how, exactly, are you supposed to pronounce the "+" in a name like "BD+05 1146"? That whole "+05 1146" part of the name is a reference to where in the skies of Earth their star is; why should anyone who actually lives there care about that kind of thing? Over six billion people live there, I'm sure at least one of them could come up with a name that's more locally appropriate.
Still, perhaps it's simply a matter of "we got used to it, and it's too late to change it now". Consider Soweto, in South Africa. The name is Apartheid-era, deriving from the abbreviation for "South-western townships". You'd think they might have come up with a better, more aspirational name now that Apartheid is no longer, but no. They're used to it, even proud of it. So "Soweto" it remains.