This starship was only mentioned in dialogue.
Additionally, according to the Encyclopedia (4th ed., vol. 1, p. 407), this ship was named for the American aircraft carrier that served as the recovery vessel for Alan Shepard's Freedom Seven Mercury spacecraft.
The name was suggested by Star Trek fan and amateur Civil War historian William F.B. Vodrey, after whom the screenwriters named the Vodrey Nebula which appeared in the same episode.
The name was derived from a mountain in New Hampshire, and various United States ships have been named USS Kearsarge, including a steam sloop-of-war during the American Civil War, and the current Kearsarge, amphibious assault ship LHD-3.