Ya know you are actually right on this one.... but it would be nice for the game to let you know. Here's what I've found out:
-Change ship name is 3,000 merits
-Registry number is 1,500 merits
-Yes, both are 4,500 merits (seems way too much, merits are kinda hard to come by and i have 160k credits...)
-Also, when I was originally naming the ship, I think I hit a character limit (would've been nice to know... warning message etc.) so I kept trying to name my ship "Tiger's Claw III" and it wouldn't work. So when the box ungreyed and I was able to try it still wouldn't accept it, but it would accept "Tiger's Claw C".... so a 14 or 15 character limit I'm guessing?
Than you have squandered your merits, at 45 i have 60,000 starfleet merits and my other character at 32 has 18000 merits. Hell even my level 11 klingon has over 3000.