Bridge Officers names are supposed to be changeable without access to the C-Store. However, last time I checked this was bugged. This is a known bug and should be fixed at some point. There's a post somewhere on the boards of StormShade specifically mentioning that Bridge Officers names should be changeable in game and that they will fix this.
Now that I thought about it some more, I didn't give one of my characters a long name at creation because it said this could be changed at any time (I think) and was optional. So I'm guessing I misunderstood this, right?
For ship registry numbers and your long name you need to pay 1500 Starfleet merits and for ship names it's 3000 credits. Bridge officers names are something similar, I don't know because I haven't used the free ones yet. For your short name, that's the one you need to buy from the C-Store, but it's not there yet.
I personally think that 3000 Starfleet Merits to change your ship name is a bit much and Merits are not exactly easy to get hold of. I made one simple mistake when naming my second ship and clicked ok without realising what I had done until it was to late. My first ship was named USS Valencia NCC 270184 and the second ship was supposed to be USS Valencia NCC 270184 - A but I accidently named it Velencia which was my mistake but can not be corrected without 3000 Starfleet Merits!