* Historically: Most of the stars we know by name were given their names by ancient civilizations (like the Greeks, Romans, Arabs) who observed the night sky. These names are often based on mythology, constellations, or their apparent brightness.
* Scientifically: Astronomers use a system of catalogues and designations to identify stars. The most famous is the Bayer designation, which uses Greek letters and the constellation name (e.g., Alpha Centauri). Other catalogues use numbers or other symbols to identify stars.
* Commercial Star Naming: Some companies offer the ability to "name a star" for a fee. These are not recognized by the scientific community or any official astronomical body. While these "names" may be registered with the company, they have no impact on the actual scientific name or designation of the star.
In short: While there are some historical and scientific naming conventions, there is no official organization that assigns names to stars. The commercial practice of "naming a star" is purely symbolic and has no scientific validity.