Greek Meaning: The name Hermione is a Greek baby name. In Greek the meaning of the name Hermione is: Well born. Stone. Feminine name derived from Hermes.In Greek mythology, Hermione was the daughter of King Menelaus of Sparta and Helen of Troy.reek Meaning: The name Hermione is a Greek baby name. In Greek the meaning of the name Hermione is: Well born. Stone. Feminine name derived from Hermes.