CAN I BUY A STAR?
 

The question is a little like asking about buying air or sunshine. Nobody owns the stars, and nobody can sell one.

There are companies, however, that will take your money and send you a certificate with some stellar coordinates, a star map and a letter.  But be aware that this is little more than a novelty item and, often, an expensive one.  There is nothing official about the name nor is there any guarantee that the star you've "purchased" hasn't been "sold" to someone else by another company in the same business.  The only organization recognized by the scientific community for naming celestial bodies is the International Astronomical Union (IAU), and they don't "sell" stars.

Now, if after reading this you still wish to pay a company for this "service," you can find surely many such companies online. 

If, however, you'd prefer more practical astronomical gift, here are a few of my suggestions: