Never established in show dialogue... The closest we have is when Sisko is shown to able to name his runabouts if he feels like it; so it may be a CO’s prerogative. Oh, and I guess Tom Paris named the Delta Flyer. But then again Janeway probably had to officially approve the naming, or just didn’t care. Mark
On a similar note: Are all shuttle craft names unique or are they just unique to each starship/starbase? I don't think we've ever seen two shuttle craft with the same name in the same place.
One of the TOS shuttles was Galileo, you'd think that a historical person like Galileo would have a full sized starship named after him. Instead of "just" a shuttle.
There may be! Just because Kirk named a shuttle that, doesn't mean there isn't a ship named that too.
I know that in one episode of TNG, I am not certain which one, that there is a shuttle named "Berman", which is the name of one of the show's executive producers. I am sure that was just done to pay homage in some way to Rick Berman, however as for how they are named in the show as far as the story is concerned, I am uncertain. In DS9 most runabout's were named after major rivers on Earth, but as for TNG, I am not sure what method is used in naming the shuttles.