I've always subscribed to the "Captain gets to choose" notion, although its more a matter of preference than based on any evidence. At the very least, I'd think the Captain would get to name his executive shuttle/yacht. I could see the Captain naming a few and letting his other senior officers each name one, too.
I don't see why you couldn't have a U.S.S. Galileo
and a Shuttlecraft Galileo
, although you wouldn't necessarily want the U.S.S. Galileo
to have a Shuttlecraft Galileo
That'd just be confusing.