Enterprise.
Because we need all the luck we can get.
What, no love for Jupiter 2?
B Ark
Not until robot/doctor marriage is made legal.
I’ll go for USS Challenger.
A proud history of scientific exploration.
If not Challenger, then Endeavor It was captained by James Cook.
Oops, I see someone has beaten me to Endeavor.
I’m good with USS Enterprise. Can’t go wrong with using the name of the most famous fictional starship and more importantly our most decorated Naval Ship that survived everything but congress.
The “Big E” for a while held off the Japanese virtually by herself while reinforcements were being built. I think the Japanese reported her sunk 6 times.
If we’re looking past our solar system, how about or nationalism(s):
Earth Ship I
We could go with the cynical name “The Vector”.
USS Sally Ride!
It’s perfect—not only because it’s the name of a great, pioneering American astronaut, but the wordplay!—sally means ‘go forth’, which is absolutely appropriate, and ride is what the astronauts will be doing on it.
USS Buzz Aldrin.
Event Horizon.
USS Leif Erickson
USS Magellan
I know we’ve used it before but all the other good names have been used as well.
What’s the purpose of the voyage? Pure exploration? Making contact with alien civilizations? Colonization? Resource survey? Military reconnaissance and security?
Manned or unmanned?
Hyperlight drive or sublight? Subspace communications or conventional?
If it’s a Starfleet-type starship, I’d say Enterprise.
If it’s a space ark, I kind of like Mayflower.
If it’s a purely military vessel, maybe Comanche.
If it’s a scientific vessel, the Beagle or Darwin.
Wasn’t that Laika’s ship?
The USS Aristotle.
Something like Newton or Copernicus would be more appropriate IMHO.
Konstantin Tsiolkovsky
Stranger
Great scientists, but they never made a voyage of discovery.
Ok, then, the Santa Maria.