Typically I label all the planets in a fashion that seems to be fairly normal in 40k, if the star's name was Rigel, for example, and it had four planets, they would be Rigel I (or Rigel Prime) Rigel II, Rigel III, Rigel IV. As I said, this seems to be pretty much the norm for Imperial naming systems.
That's a common sci-fi trope, but if you look at the maps of the Calixis Sector, Koronus Expanse and Jericho Reach, you'll find relatively few worlds named like that. All manner of names are used, with no particular convention to it - simply pick whatever seems appropriate at the time. You may find a star cluster that contains worlds called Piety (established by pilgrims who were thrown off course during their journeys, and who see their finding of a habitable world as divine provenance), Hamaskis' Fall (the last of seven worlds conquered by Rogue Trader Durantar Hamaskis, and the world he was buried on) and Hurathain (named by pre-industrial human inhabitants, translation unclear as it appears to be an an archaic form of the native language).
That is often the trick with names... when people give something a name, that name often means something to the people who gave it, and even if you start with the name and work backwards, figuring out why the world was named that way is often an interesting way to get the creative juices flowing.
Personally, in my Rogue Trader game, I only name worlds that already have inhabitants or claimants, and I don't expect my players to abide by those anyway. If my players find a habitable world in the depths of the Expanse, they're free to name it whatever they want.
If you're carrying on with the [Star] [Number] type system, then naming moons is easy - add another signifying digit (a letter instead of a number helps keep it clear) somewhere in the name. So, the 2nd moon of the fourth planet in the Tibon system could be called Tibon IV B, Tibon 4-Beta, and so on. Putting the planet's identifier as a word (Alpha, Beta, Gamma, etc, or Primus, Secundus, Tertius, etc) also works to keep the name distinguished from the numbering of the moon - Tibon Delta II, or Delta Tibon II, for example. Even with that method, there's a reasonable amount of room for variation.
Writing Credits for Fantasy Flight Games: Into the Storm, Edge of the Abyss, Battlefleet Koronus, Hostile Acquisitions, Black Crusade Core Rulebook, First Founding, The Jericho Reach, The Soul Reaver, Only War, The Navis Primer and Ark of Lost Souls