In the case of stars, the IAU does not allocate individual names. It is simply not a practical method for keeping track of hundreds of millions of stars. Catalogue numbers are used instead. A few hundred of the brightest stars in the sky have traditional names, mostly handed down from centuries ago. The most well-known of these names, such as Sirius and Polaris, are often used by astronomers, but strictly speaking they are unofficial.
Some commercial organisations offer to name, or 'redesignate' stars for payment.
The certificates they issue, and the names they allocate, have no official status of any kind. They are not used or recognised by astronomers. There are also commercial enterprises offering to 'sell' plots of land on the Moon, and on other moons and planets in the solar system. These claims, like the star names, are not recognized by any authority. The Royal Astronomical Society supports the IAU's position on the practice of 'selling' star names or land on moons and planets and dissociates itself from the activities of the commercial organisations engaged in these businesses.