The international Astronomical Union or IAU is the authority that assigns the official names to celestial bodies and the surface features of those bodies. It is the only recognized naming organization and if it doesn't approve and assign a name, the name doesn't stick. There are firms that offer to let people name space objects for a fee.
The IAU recently issued a statement that notes it would not assign an official name to a celestial body or surface feature on a planet that legitimizes a purchased name. It appears that the IAU is specifically talking about a service from a firm named Uwingu that has a campaign that allows people to name craters on the surface of Mars.
Uwingu launched a project on February 26 allowing people to name 500,000 craters on the surface of Mars that don't have names. The cheapest craters to name are the smallest and start at about $5. Wingu stipulates that it is the place for what it calls "people's choice" names, not the official names.
Uwingu is very specific in that it isn't seeking approval from the IAU to use any names it sells as the official name of features. Rather, the company is creating a people's map of Mars using the names it sells. However, the features on the surface of Mars that the IAU has already named are not available for renaming via Uwingu.