Autogenerated names look OK, but to me they also all look the same. I don't look at them and see a name, I see "random stuff" and "more random stuff".
I would actually be a big fan of using Alpha, Beta, Gamma even in smaller galaxies, as long as you used them on stars close to each other.
Naming stars randomly makes them harder to remember, naming clumps of stars makes them easier to remember.
"Oh, a Centauri, the centauris are over here."
I am also a huge fan of seed reliability, to the point that I think we should roll our own code. Remember, we aren't trying to make something secure, we are trying to make it reliable, so as long as it looks random and works the same everywhere it's perfect.
I don't know how you currently have it coded, but I think the seed needs to be reset for each category, to maximize predictability, so that for example, if two games use the same seed and have the same number of stars, but have different starlane and monster frequency, the higher frequency one will have the exact same monsters in the same places as the lower frequency one, plus a few more.
Something like taking the simple function and feeding it the seed XORed to "monsters", then reseeding XORed to "specials" next, and when playing the game, as much as possible for random events XOR "turn12" and "sys109" to the seed so that the random events play out the same each time.
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