General rule of thumb: Characters in the Sailor Moon universe are often named for celestial bodies, which in turn are named for gods and heros from Roman/ Greek mythology. So, look through the names of the moons of the planets, or other names associated with those planets, find any that are appealing to you, then look up the corresponding mythological character. Then, when you learn about the traits or adventures of those characters, you could apply those to your characters via powers, backstory, or whatever.
For instance, it is known that Helios is of the sun. His mother (I believe) was Eos, goddess of the dawn. So, from here you could look up facts about Eos and evolve a character from what you learn. (Maybe Eos can be queen of the Sun Kingdom and is the mother of Helios.)
If you also require civilian Earth names (like in Japanese), you can then look up the meaning of each name you find, or other related names and terms, then search for the translation of that word to match the corresponding language. For instance, while in Japan Eos could be named Hikaru (light), Asa/ Asako (dawn), Kagayaku (shining), etc.
Here are a couple of websites to get you started.
http://www.fief.org/kathleen/Moons/Moons.html (for heavenly bodies)
http://www.theoi.com (for mythology)
For fictional planets, I would suggest learning about other mythology characters and using their names, double checking to see whether a heavenly body was already named for them. Also beware some bodies are named not for heros but the discoverer of that body (i.e. real people). This shouldn't necessarily prevent the use of such names, but it's something to keep in mind for story building purposes.
(Also, last I heard we now have a planet Xena floating around somewhere, who is named for a TV show character. So, who's to say your fanfic can't also have a Sailor Xena, a warrior princess who yodels and throws a chakram.
And if you don't want your fanfic to be classified as a "crossover" you could just borrow bits and peices of the show, alter several features, and then basically treat the show as another reference from Greek mythology.
Thus, instead of say, including Gabrielle the queen of the Amazons as another senshi, you could give Sailor Xena a guardian cat named Gabrielle who came from one of the asteroids belonging to the Quartette.
)
(Note: When you get to the Saturn kingdom, be sure to understand the difference between the names Chronos and Cronus. Two totally different characters with totally different powers and origins. There is a TON of misinformation on them where people assumed they are the same character, and some of it is verrrry convincing. But they're not. Trust me on this.)