The Klingon captain in “Errand of Mercy” was Kor. Played by John Colicos, Kor becomes the military governor of Organia after Klingon forces occupy the planet during the Federation–Klingon war.
Kor is more than a one-episode antagonist. The character later returns in Star Trek: Deep Space Nine, where he is portrayed as an aging Klingon warrior in “Blood Oath,” “The Sword of Kahless,” and “Once More unto the Breach.” Those appearances establish him as one of the earliest recurring Klingon characters in Star Trek.
A common mix-up is confusing Kor with Kang or Koloth, who are also major Klingon officers from the original series era. Kang appears in “The Day of the Dove,” while Koloth commands the Klingon cruiser in “The Trouble with Tribbles.” Garth is not a Klingon captain; Garth of Izar is a human Starfleet captain featured in “Whom Gods Destroy.”