My ideas for that is naming like a mix between that you said and the exoplanets in RL, so you have the name of the player/org who discovered the solar system / group of planets, then the number of this solar system, and then the letter for the planet.
For example, I just discovered a new planet (the third) in the sixth solar system I found. The name would be ttcraft0-6C. And for the most crowded/known planets, there would be a "custom" name. For example the first planet would be NQ-1A but the devs gave it a name (I don't remember it ^^)
For moons, let's say I find 2 moons for my planet. Their names (in the order I discovered them) will be ttcraft0-6Ca and ttcraft0-6Cb for example.
Continents and oceans : I don't really know ^^
Territory : same thing
+ Cities : custom, or if you can't find a good name : [planet]-[number of the city]