It is important to understand what your money actually buys: A Star by Any Other Name - Kielder Observatory

The treaty also says that that governments are responsible for public and private organisations that operate within their country, Kielder Observatory Can I buy a star? - American Astronomical Society

Can include framed documents, jewelry with coordinates, or "twin star" naming for binary systems. The Scientific and Legal Reality

In reality, you cannot legally "buy" a star, as international law prohibits the ownership of celestial bodies. However, a thriving commercial market allows you to a star for prices ranging from $20 to over $100 . The Cost of a "Symbolic" Star

Includes an entry in a private database and a digital certificate.

If you are looking for a commemorative gift, commercial registries offer various packages: