Many web sites and magazines, especially ones related to astronomy, contain advertisements urging you to buy or name a star or other celestial object
. Such advertisements always emphasize the "official" nature of their service, promising to keep a record of "your" star in a registry available to anyone who wants to know the names of the stars, who will hopefully stumble across "your" star and the name you gave it. These "services" are all scams.
Star names are based on historical use and precedent, and no organization has the right to sell them. In fact international law forbids the ownership of celestial objects, in or out of the Solar System by any government or individual. So if you really want to name that big, bright thing that rises in the east every morning after your favorite uncle, or "give" it to your current sweetheart, there's no reason you can't do so; but whether you do it yourself or pay someone to do it for you, everyone else will still call it the Sun, and rightly consider it just as much theirs as yours.