Official names for celestial objects are assigned by the International Astronomical Union. The system in naming varies depending on the type of object. Often there is an official procedure for assigning temporary designations as soon as possible after an object is discovered and later on a permanent name.
Some commercial companies purport to allow you to name a star. Normally, they send you a nice certificate and a piece of a star atlas showing “your” star. There is a statement on star naming that IPS Council approved on the June 30, 1988.
Below is the official IPS Statement in selling star names:
The star names recognized and used by scientists are those that have been published by astronomers at credible scientific institutions. The International Astronomical Union, the worldwide federation of astronomical societies, accepts and uses _only_ those names. Such names are never sold.
Private groups in business to make money may claim to “name a star for you or a loved one, providing the perfect gift for many occasions.” One organization offers to register that name in a Geneva, Switzerland, vault and to place that name in their beautiful copyrighted catalog. However official-sounding this procedure may seem, the name and the catalog are not recognized or used by any scientific institution. Further, the official-looking star charts that commonly accompany a “purchased star name” are the Becvar charts excerpted from the _Atlas Coeli 1950.0_. [Other star atlases such as _Atlas Borealis_ may be used instead.] While these are legitimate charts, published by Sky Publishing Corporation, they have been modified by the private “star name” business unofficially. Unfortunately, there are instances of news media describing the purchase of a star name, apparently not realizing that they are promoting a money-making business only and not science. Advertisements and media promotion both seem to increase during holiday periods.
Planetariums and museums occasionally “sell” stars as a way to raise funds for their non-profit institutions. Normally these institutions are extremely careful to explain that they are not officially naming stars and that the “naming” done for a donation is for amusement only.