Agapet is not a popular first name for women and an equally uncommon surname or last name for both men and women. (1990 U.S. Census)
Agapet \a-ga-pet\ as a girl's name is a variant of Agatha (Greek), and the meaning of Agapet is "good, honorable". The baby name Agapet sounds like Agapit. Other similar baby names are Agape, Agapi, Agappe and Agate.