Odyssey

NASA has given following names to manned spacecrafts.

Mercury program:
Mercury-Redstone 3 Freedom 7
Mercury-Redstone 4 Libery Bell 7
Mercury-Atlas 6 Friendship 7
Mercury-Atlas 7 Aurora 7
Mercury-Atlas 8 Sigma 7
Mercury-Atlas 9 Faith 7

Gemini program:
Gemini 3 The Molly Brown
Gemini spacecrafts were unnamed. The Molly Brown was nickname given by Gemini 3's Commander.

Apollo program: (CSM / LM)
Apollo 9 Gumdrop / Spider
Apollo 10 Charlie Brown / Snoopy
Apollo 11 Columbia / Eagle
Apollo 12 Yankee Clipper / Intrepid
Apollo 13 Odyssey / Aquarius
Apollo 14 Kitty Hawk / Antares
Apollo 15 Endeavour / Falcon
Apollo 16 Casper / Orion
Apollo 17 America / Challenger

Space Shuttles:
Challenger
Columbia
Discovery
Atlantis
Endeavour

Most of the names comes from naval ships, popular culture, have some patriotic meaning. Only small number have Greek background. As it's previously said NASA has history to reuse names to new spacecrafts. Spacecraft launched by NASA could very well have one of those names mentioned above. This would also give some credibility to new spacecraft.

Challenger and probably Columbia too might be out of question for obvious reasons. Some might be a little bit corny. As I said in one comment, my personal favourite is Odyssey. It has some dark history behind it without being catastrophical accident. Many knows Apollo 13 name but not so many knows it's Command Module's name. So it could be considered nice joke for space history buffs.

btw USS prefix is used by USN so I can't see why would NASA use it. No other American agency than NASA (if even NASA) has enough resources and knowledge (even in 2018) to launch manned mission to moon.

Edit: Removed Enterprise from the shuttle list.