There is a sharp distinction between how stars are officially named by scientists and how they are "sold" by private companies: Can I buy a star? - American Astronomical Society
While you can pay a company to "name" a star, you cannot legally buy or own a star. Purchasing a star from a commercial registry is a rather than a recognized astronomical or legal transaction. Scientific vs. Commercial Reality can i buy a star
There is a sharp distinction between how stars are officially named by scientists and how they are "sold" by private companies: Can I buy a star? - American Astronomical Society
While you can pay a company to "name" a star, you cannot legally buy or own a star. Purchasing a star from a commercial registry is a rather than a recognized astronomical or legal transaction. Scientific vs. Commercial Reality