Ship names are NOT unique, but as far as I can tell, registry numbers are. You'll need to add the letter afterwords to keep the same reg number, or decommission your old ship and use it's registry number.
I've gotten enough merits to be able to rename the ship, but when I try to use the same name as my other ship, nothing happens. I hit the Ok button and the game refuses to set the same name as my first ship. Anyone else having this problem?