In Star Trek, what is the name of Captain Kirk's starship?

Captain Kirk's starship in Star Trek is the USS Enterprise, specifically the USS Enterprise NCC-1701.

The Constitution-class Enterprise is the primary setting of the original Star Trek television series, which aired from 1966 to 1969. Under Captain James T. Kirk, its crew undertakes a five-year mission to explore strange new worlds, seek new life and civilizations, and expand the Federation's knowledge of space.

The ship is not unique within the franchise: later vessels also carry the Enterprise name. After the original ship is destroyed, Kirk receives command of the USS Enterprise NCC-1701-A in Star Trek IV: The Voyage Home. Later series and films introduce further versions, including the Enterprise-D and Enterprise-E.

That history explains why “USS Enterprise” is the fair answer to the question, even though NCC-1701 is the precise registry of Kirk's original starship. The other options belong to different Star Trek ships and captains: Discovery, Defiant and Voyager are not Kirk's original command.