Several companies claim to sell people the right to name a star in the sky, complete with a certificate and coordinates. However, these hold no weight among astronomers.
According to Space.com, professional astronomers only recognize names and star numbers issued by the International Astronomical Union. Since the IAU does not sell star names or license anyone to do so, star registries hold no right to name a star.
Official Star Naming
In general, the IAU gives stars numerical identifiers, except for extremely important stars traditionally known by a name, such as Sirius, the brightest star.
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Exoplanets and Other Heavenly Objects
In addition to stars, the IAU also handles the naming of recently-discovered planets outside the solar system, as well as galaxies and other astronomical objects. Commercial registries for exoplanets therefore hold no official weight with astronomers.
Just because star registries do not have the power to officially name a star does not mean that "naming" a star has no worth. Some people enjoy the novelty of naming a star and registries may pique interest in astronomy.