It's a minor bother, but still a bother nonetheless. All dialogue windows, and even my toon's info sheet list my ship's name as whatever I named my small craft when I'm not flying it, and show my ship's name as whatever I named my primary starship when I'm not flying that.
This has been a problem for a while. Also a problem if you try to repair a ship injury in a STF before respawn it usually comes up with my shuttle. I have to go and select the ship then repair. I have reported this myself several times in the past year or so and no acknowledgement or mention of a fix.
Somebody suggested renaming your shuttle to come alphabetically after your ship name. I have 8 toons and did this with 6. It worked on a couple but not all. I even dismissed and reclaimed both the shuttles and the primary ship and that did nothing to fix the problem.
Honestly I would love to just go back to the old system where you manually had to change to shuttles at a shipyard or your ship interior if it is going to screw with the game this way.