For my Leviathan character, his chocobo's name is Kharble. Named after a fellow Exalted player. He even picked the color (Raptor Blue).

My character on Behemoth has her chocobo named Creos. Named after an Exalted player's fire Aspect Dragon-Blooded. (No, not Kharble, different player.)

And, lastly, my character on Lamia has her chocobo named Katuali. Also named after an Exalted player's character, this time a Lunar with a snake totem. (Also not Kharble.)