You've probably seen on the Internet that people are offering to allow you to name a star for a price. They say the star will be officially what you call it. The truth is, that it won't, it'll be called whatever it is recorded by the I.A.U. or other stellar organisations.
Take for instance the star, Hip 108471, an orange to red star in the constellation of Pegasus. Its a faint star, not one that is visible without binoculars. You pay a star naming service to call it after yourself, so lets say you are Simon Forsyth. They send you a decorative certificate stating that HIP 108471 is now known a Simon Forsyth.
You tell your family and your friends that you have a star named after you. You want more information so you write to N.A.S.A. and ask for everything they know about the star. They'll write back saying, sorry, never heard of the star Simon Forsyth, they might even write back and give you details about HIP 108471 if you also included the "old name".
The money you've spent is worthless, it'll just have been for a professional looking certificate and nothing else. It'll just be a gimmick, nothing else. All that hype will have been for nothing.
You can call the star whatever you want but it'll only be known by you, your friends and family, not the wider community. The only time you can name a star is when the I.A.U. announce a competition to name stars. When they run a competition, the new name has to follow a strict set of guidelines. One of those is that it not be offensive to one or more people.
It was only recently that Rigel was officially known as Rigel, before it was known as Alpha Orionis or Hip 24436. The Alpha Orionis is the Bayer catalogue name for the star and the Hip number is the 24436th star studied by the Hipparcos satellite. Internally to the site, the star is known as UG7 but me telling anyone else, they won't know what I'm talking about.
There are some stars out there such as Tabby's Star which is named after a person who led an investigation into the star but those stars are rare to be named after someone. Another example is Teegardens Star, named after the scientist who studied it. When I say studiy it, you really have to study it, not just write a small paper about it. You can't also rename a star, saying good bye to Rigel and changing it to something else.
You can have an asteroid or a comet named after you but you have to discover or examine it first. Take for instance Comet Halley, the most famous comet in the world. Halley's Comet is named after Sir Edmund Halley who predicted its return and when it returned, it was named after him. Amateurs are at disadvantage given the range of telescopes that professions have to make these new discoveries.
Another way to have an asteroid named after you is to have it dedicated to you. Anne Frank asteroid is dedicated to the young Jewish girl who hid from the Nazis during the Second World War in the Netherlands and wrote a diary about her hiding. Just before the war ended, the Nazis discovered her and sent to a concentration camp.
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You can decline to give a name which if that is the case, the comment will be attributed to a random star. A name is preferred even if its a random made up one by yourself.