Official names for celestial objects are assigned by the International Astronomical Union (IAU). Procedures vary depending on the type of object. Often there is a system for assigning temporary designations as soon as possible after an object is discovered and later on a permanent name. Stars are never named after people. Asteroids are named by the discoverer. Comets are given the discoverer's name (e.g. Halley, or Hale-Bopp). Planetary surface features are sometimes named after historical figures (e.g. crater Copernicus on the moon).
Some commercial companies purport to allow you to name a star. Typically they send you a nice certificate and a piece of a star atlas showing "your" star. The following statement on star naming was approved by the IPS Council June 30, 1988.
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.
Bright stars from first to third magnitude have proper names that have been in use for hundreds of years. Most of these names are Arabic. Examples are Betelgeuse, the bright orange star in the constellation Orion, and Dubhe, the second-magnitude star at the edge of the Big Dipper's cup (Ursa Major). A few proper star names are not Arabic. One is Polaris, the second-magnitude star at the end of the handle of the Little Dipper (Ursa Minor). Polaris also carries the popular name, the North Star.
A second system for naming bright stars was introduced in 1603 by J. Bayer of Bavaria. In his constellation atlas, Bayer assigned successive letters of the Greek alphabet to the brighter stars of each constellation. Each Bayer designation is the Greek letter with the genitive form of the constellation name. Thus Polaris is Alpha Ursae Minoris. Occasionally Bayer switched brightness order for serial order in assigning Greek letters. An example of this is Dubhe as Alpha Ursae Majoris, with each star along the Big Dipper from the cup to handle having the next Greek letter.
Faint stars are designated in different ways in catalogs prepared and used by astronomers. One is the Bonner Durchmusterung, compiled at Bonn Observatory starting in 1837. A third of a million stars to a faintness of ninth magnitude are listed by "BD numbers." The Smithsonian Astrophysical Observatory (SAO) Catalog, The Yale Star Catalog, and The Henry Draper Catalog published by Harvard College Observatory all are widely used by astronomers. The Supernova of 1987 (Supernova 1987A), one of the major astronomical events of this century, was identified with the star named SK -69 202 in the very specialized catalog, the Deep Objective Prism Survey of the Large Magellanic Cloud, published by the Warner and Swasey Observatory.
These procedures and catalogs accepted by the International Astronomical Union are the only means by which stars receive long-lasting names. Be aware that no one can buy immortality for anyone in the form of a star name.