You can name your ship whatever you want. Just go to the Status tab for your ship and there is a button to rename.
Note: If you want to name your new ship the same name as your old ship, you must change the name of your old ship to something else first. Apparently two ships cannot have the same name, even if they are owned by the same person.
When I did mine (naming) the hull did not show the correct name I selected in space, so I just went back to the spaceport and re-applied the hull design and re-saved it...then it worked so just a quick FYI for renaming purposes if your selected name is not appearing correctly.