We have several names (many many names) as options. They've all got some meaning:
Canopus: Acted as southern North Star for navigation. In mythology Canopus is said to be the the steersman of the Argo, the ship of the Argonauts. He was also the steersman of king Menelaus' ship who started the Troy War in order to retrieve his stolen Helen.
Capella: "little she goat" in Latin. The star represents Jupiter's goat, Amalthea. Jupiter accidentally broke off one of her horns, which later became the Cornucopia.
Caph: Arabic for "palm".
Castor: Mortal twin of the "Gemini" constellation. Means "beaver" in Latin and Greek.
Castula (Nu Cephei): Part of a multiple star system in the Cepheus constellation.
Cebelrai: Arabic for "shepherd dog"
Celaeno: Harpy, lover of the west wind. Her name means "darkness" as one of the three aspects of a storm. An amazon killed by Heracles was also called Celaeno. Also Poseidon's wife was named Celaeno.
Chara: Meaning "joy" in Greek, this star's system is one of the top candidate for extraterrestrial life. Its distance to our sun is 27,4 light years.
Cheratan: Arabic for "two small rips". 170 light years separates us from that distant star.
Cor Caroli: "Charles' Heart" after Charles I of England who died after the English Civil War 1651.
Cujam: Means "club" in Latin and is in the constellation of Hercules.
Cursa: Arabic for "footstool of the giant". It's a star, which is 90 light years away from Earth and part of the Eridanus constellation.
