If you are looking to "buy a star," it is important to understand that you cannot legally or scientifically own a star or its official name. All stars are named and cataloged by the using alphanumeric designations for scientific purposes.

Best for a romantic or memorial gift. You receive a certificate and coordinates, but the name is only recognized by that specific company.

If you proceed with a commercial gift, compare providers based on the "extras" they offer: Rules to Name a Star - IAU Office for Astronomy Outreach

The IAU occasionally holds public campaigns, such as NameExoWorlds , where you can suggest names for newly discovered planets and their stars for free. These names become scientifically official.