It was said in FS1 that Vasuda Prime was the fourth planet in the system. So "Prime" can just refer to any inhabited planet I guess.
But I think, for instance, "
Planet Alshain" sounds much better than "Beta Aquilae Prime" or "The largest inhabited moon of Beta Aquilae II".

I've given a bunch of planets in ETF proper names, and gone through the systems trying to figure out which ones are inhabited in the FS universe, and how that is so based on actual astronomical data:
Antares IV-a: Gulnara (the closest transliteration possible since it was originally named by the Vasudans); basically, it's a dustball even by Vasudan standards. Antares changed hands lots of times, but there was only one T-V War battle over Gulnara. Most Gulnarans (Terrans and Vasudans alike) are fairly stoic about war in general and refused to leave even when the Shivans were overhead.
Beta Cygni V-a and V-c = Albireo and Alminhar. Like Alshain in Beta Aquilae I named 'em for the original proper name(s) of the system.
Ribos IV retains its numeral as per the command briefing in FS1.
Delta Serpentis A: Delta Ser is a binary system, but the secondary star's things are not named. The first star's planets are named (in order) Eikan, Tensho, Konin, and Genei, after Japanese imperial eras, since most of the first settlers there were of Japanese descent. Tensho is entirely water-covered, but it is inhabited, and produces quite a bit of food. I'll elaborate this Saturday with my next Tech Entry.

Both
planets of Wolf 359 are named. Respectively, they are Ymir and Lupus.
Luyten's sole planet is Luyten Prime. Most of the other planetary material got ejected over time, either due to the binary system's orbits or the flares they both give off.
But that's just my ideas. Arr.
