Let's see now, how can one own a star? That's sort of like asking if you can buy air or sunshine. Because they exist universally, stars belong to no one, so logically, if no one owns them, you would think that no one could sell them. Literally speaking, you can't own a star. They belong to everyone who sees them.
Even if you name your star or have someone else name your star, astronomers will not use that name. Read below how stars receive their names. However, you can have companies send you a certificate with some stellar coordinates, a star map and a letter. This will help you locate the stars that you might want to consider your own. Note that you will be receiving just an expensive novelty item, though. No company can make your name official or guarantee that you indeed have bought a star that someone else hasn't already bought through another company in the same business.
Approximately si thousand stars light up our night sky. If dealers indeed report these star names correctly, all of the stars have an owner. Therefore, if you want to own a unique star on your own, you're out of luck: you probably won't even be able to see it.
Below you will find a summary of the visit I received from one who purchased a star name from a company. See what he got for his money.
Most star names come from antiquity. In fact, The Almagest, one of the earliest star atlases, dates back to the third century BC. Today, however, the International Astronomical Union governs the names of stars, planets, moons, and other celestial bodies. Their power comes directly from an agreement with the world's astronomers and international treaty. When you buy a star name from a company, the IAU will not recognize it.
Where do comets and asteroids get their names? Generally speaking, comets are named after people or machines who discover them. For example, Alan Hale and Thomas Bopp received credit for simultaneously discovering the comet that we now call by their names. The comet LINEAR received its name from the space probe that discovered it.
Asteroids don't have the luxury of real names. Instead the IAU generally gives them a numeric designation. In the past, however, the IAU has given asteroids names suggested by the one who discovered the asteroid. Scientists, artists, and even musicians have found derivatives of their names tacked unto an asteroid. You never know. Maybe an asteroid has your name tacked unto it.