Click the links below:  We'll be registering our girl as Cleopatra

Cecrops

Cedalion - Guided Orion, the hunter.

Centaur

Cerberus - Watchdog of the afterlife.

Chaos - Seems like a bad name for a hunting dog.

Chiron

Chronos - Father Time

Cratos - Strength

Crius

Cronus

Cadmus

Caeneus - Hunted with Artemis

Calchas

Castor

Cepheus - Hunted with Artemis, who leads the Calydonian Hunt

Cinyras

Cychreus

Caesar or Czar

Cabal King Aurthur's dog

Everything that starts with C