The Klingon Bird-of-Prey stolen by Kirk and his crew was named HMS Bounty.
The crew captured the vessel after defeating the Klingon commander Kruge in Star Trek III: The Search for Spock. They used it as their only escape craft after the USS Enterprise was destroyed, then carried it into Star Trek IV: The Voyage Home. Dr. Leonard McCoy suggested the name HMS Bounty, referencing the famous British ship involved in the 1789 mutiny.
The renamed vessel became essential to the film’s plot. Its cloaking device helped the crew travel undetected, while its ability to “slingshot” around the Sun sent them from the 23rd century to 1986 Earth. There, they searched for humpback whales to answer a mysterious probe threatening the planet.
The main mix-up is assuming HMS Bounty was the ship’s original Klingon name. The film emphasizes the Federation crew’s new name; proposed or licensed-fiction Klingon names are not the standard cinematic answer.