In the year 2006, astronomers made two significant chances in the nomenclature of our solar system. Pluto was downgraded to a dwarf planet (I'm still not over that, mind you), and a slightly larger Kuiper Belt object that was previously known as "Xena" was given the official name Eris. But does this name really fit the usual naming rules for planets and planetoids? The names we use for the six planets visible with the naked eye come from the Romans. They're all named after gods, and while the fact that the Romans appropriated much of Greek mythology means that all of these gods had their Greek counterparts (Hermes for Mercury, Aphrodite for Venus, Ares for Mars, etc.), it was the Latin names that became the standard ones for our Sun-orbiting neighbors. When William Herschel discovered Uranus in 1781, he called it "Georgium Sidus" after the King of England, but its current name became the most commonly used one in the following century. While I'm not entirely sure of this, I've seen it suggested that the reasoning behind the name Uranus is that, in Greco-Roman mythology, Jupiter is the father of Mars and Saturn of Jupiter, so it only made sense to name the next planet after Saturn's own father. The odd thing about that, however, is that the Latin name for the primordial Greek sky deity was Caelus, with "Uranus" simply being a Latinized version of the Greek name Ouranos. Similarly, Eris is also a Greek name, with her Latin equivalent being Discordia. I believe the only rule for planet-naming is that they have to have the names of Greco-Roman gods, so these don't technically break that rule, but it seems like giving them the Latin names would have made things somewhat neater. The names of other planet-like objects have a mixture of mythological names and others, and I have to say it's a little unfair that significant deities like Juno and Minerva get no more than asteroids. Incidentally, both Vulcan (okay, actually "Vulcano") and Romulus, which were used for planets in other star systems in the Star Trek universe, are also both asteroid names.
Incidentally, according to the International Astronomical Union, stars don't officially have names, just catalog numbers. These are mostly determined based on constellations, which is a rather geocentric method, but I'm sure any other would be too insanely complicated. Traditional names are still in use for the brighter stars, however, many coming from Arabic, but others from Latin,Babylonian, and Chinese. There are also companies that name stars after people for money, but these are in no way official.