Giving away a star named after someone special to you is a symbolic novelty gift. Global Star Registry offers a service to name real stars. The stars that are named through Global Star Registry is not recognised in an official body though they are recorded in a book, which is registered in the copyright office of the United States of America. Each star name will be filed and registered once only. It is not possible to actually own a stellar object as nobody (or everybody, depending on your way of looking at it) has ownership. A star is essentially a ball of boiling gas trillions of miles away, so ownership is hardly a viable option anyway!