While it is not possible to legally or scientifically "own" a star, you can purchase through various commercial registries. These services allow you to assign a name to a specific celestial coordinate and receive a commemorative gift package, though the International Astronomical Union (IAU) does not recognize these names for official scientific purposes. How Star Naming Services Work
: The company provides a certificate of registration, a star chart with coordinates, and often a mobile app to help you locate the star in the sky.
: Your chosen name is recorded in the company’s private catalog, such as the International Star Registry’s copyrighted book, "Your Place in the Cosmos". Available Gift Packages and Pricing
Prices generally range from approximately depending on the materials and features included. Can I buy a star? - American Astronomical Society