You may rename your starship at any branch of the Starship Registry, found at all capital spaceport facilities. Renaming will charge you a fee depending on the class and base value of the starship.
To rename your ship, have it on the nearest landing pad and use the RENAME command inside a starship registry.
Renaming a ship will automatically post a public message to the message boards, so that you cannot, for instance, commit an act of piracy and then make your ship untraceable by changing its name.
If you are looking for help on renaming your character, please read the Name Change help file.