It is difficult to say enough bad things about this practice---not about the buying part, but rather the selling part. Technically, none of the places that purport to sell you a star/star name are actually doing so. What they are selling you is the right to have your name and your star name published in a book which is registered withe U.S. Copyright Office. Uhm, most books that are published are registered with the U.S. Copyright Office. Oh yes, and they will give you a nice piece of fake parchment with your star name as a receipt. If you are looking for a novelty gift, that's all well and good and I don't want to stop you. But if you think you were about to buy (or perhaps already bought) anything with some official standing, read anon....
- Buying A Star FAQ is maintained by Bill McClain, Jim Craig, and Bob Martino and has some useful information what you can and can't do. There are also useful links to other information (including the links below) on star naming.
- The International Astronomical Union (IAU), the official keeper of real star names, has an official press release on Buying Stars and Star Names where they also describe things you can do that would do a better job of promoting science.
- IPS Official Statement on Star Naming also has information on star naming practices.
Another resource sent to my by Amy Martin, a science education major, is this set of links with the unwieldy name of A Guide to Naming A Star After a Loved One which includes some of the above. The site itself is (ahem) a dating site, and since many of the links cover the facts of star naming and since advertisement for buying a star often seems to involve an appeal to romance, I think they're at least doing their members a favor by injecting a note a reality.