Despite the ship's name being spelled as "T'Acog" in both the Encyclopedia and the episode's shooting script, K'Nera mispronounces the ship's name as "K'Atog" in the only occasion when the ship's name is mentioned in dialogue.
According to the Star Trek: Star Charts (p. 65), a possible origin for the name of the ship was the T'Acog star system. This was a single star system. T'Acog was a B class star with a magnitude of +7, which was 1/10 the brightness as Sol. This system was the site of a historic battle. It was located in or near Klingon space.