Having finally purchased an Aeon timeship, I actually paid attention to some shuttle stuff in the game for a change. In doing so, I noticed the following bugs concerning shuttles:
1. Renaming a shuttle can cause the shuttle's name and registry to appear on your normal ship's hull. I've only been able to correct this by renaming the normal ship twice, once to a new name, then back to the old name.
2. Setting a default small craft now makes that appear as your current ship in both the login screen and in game player profile window...even when not using it! There does not seem to be any way to work around this bug at the moment.
3. Switching between ships utilizing a ship interior can also change the name appearing on your normal ship. It should be noted that this is a cosmetic change, and does not impact any of the in game status screen.
What I personally noticed is that the ship that displays on your character select screen is the one that you purchased/claimed later. For example, if you own a ship and purchase a new shuttle, then it's the shuttle that's going to be displayed. But if you select a shuttle that was purchased before the ship you're flying, it's the ship that's going to be displayed.