Planet names, like
star names, come from a variety of sources. Unlike stars, we haven't given "proper names" to any planet in any star system other than our own, so the only "in real life" planet names in ED are the ones in Sol system.
Planets in "FE2 legacy systems", that either have old FE2 procedurally-generated names or are one of the couple dozen in-real-life stars that were on the old FE2 starmap, will usually carry over the procedurally-generated planet name that was given to them by the FE2 random name generator; this basically picked a planet name from a fairly short list: New Africa, New America, New California, Capitol, Diamond, Topaz, Emerald, Experiment, Conversion (those last two were reserved for terraformed worlds), as well as "XXXX's world" where "XXXX" was selected from a fairly short list of available names: Amundsen, Kawasaki, Miller, Duval, etc; "World" also had a few possible substitutes, like "Colony" and "Eden". With a relatively large number of planets and a small list of possible planet-name combinations, it was not uncommon for two or more planets in FE2 to have the same name; this is why there are four planets named "New California" in ED. There were a couple of other hand-carved systems in FE2, like Eta Cassiopiae, with hand-named planets in them.
Some planets and star systems in ED have been manually named by FD for reasons of their own. Every object in the 17 Draconis system, for example, is named; the ELW is called "Paradiso". This system was created like this by ED to record a promotional video for a game event, and they wanted everything in the video to have a cool-looking name.
Finally, we have the backer names. Early backers of the game could buy the right to name stars, planets, space stations etc.. Some of these are obviously placed by backers, even if the derivation of the name is not obvious at first glance. In the Bast system, for example, the only planet is the terraformed ELW called "THFC est1882", which sounds like a weird catalogue code until you realise (or it is pointed out to you) that the Tottenham Hotspurs Football Club was established in 1882. It should perhaps also be pointed out that this football club's home ground was (until recently) White Hart Lane, so it is not a coincidence that the only space station in this system is named "Hart Station".