I'm having same problem and would like some info please. A couple of friends I was on Teamspeak with said they could change their ship names just fine. I also got the NX designation from the deluxe purchase and it shows up in the pull down, but it wont let me save it with my ship name.
Well maybe you entered a name that already exists in game. I guess there cant be two ships of same name in game. I tried for example naming my new ship (t2) the same as the first one (t1), but didnt work. When I entered other name, it renamed. Later I bought another type of t2 ship and tried to rename it - and I again wanted same name as my t1 ship was - didnt work. But after that I dismissed (destroyed) the old t1 ship and voila... the t2 ship could be named the same name as t1 ship previously had. So I think thats it - NAME TAKEN.
I would also like to change my ship's name. I too tried to name my ship unsuccessfully, until I randomly hit, and got a 'Novssss' named ship (which is stupid name mind you). I too would like to be able to rename it properly.