As with several other characters in Rise of the Argonauts, Pan appears to be named after and partially inspired by a character from Greek myth (in this case the demigod Pan, lord of Satyrs), but is not meant to actually represent that character. The biggest indication that this is not the same person as the Pan of legend lies in Jason's quest itself; he is tasked with finding members of the bloodlines of the gods Ares, Hermes, and Athena and bringing them back to Delphi; the mythological Pan is the son of Hermes, which would make the entire adventure on the island of Saria to find a distant descendant of Hermes a complete waste of time.
This Pan is a humble servant of the compassionate sun god Apollo, living on the hidden island of Delphi with the unaging Oracle, Appoline. At the Oracle's request, Pan joins King Jason of Iolcus and his best friend Hercules as an Argonaut, a member of the crew of the mighty ship Argo.
In Jason's quest to find the Golden Fleece, a legendary artifact which will allow him to raise his murdered wife Alceme from the dead, Pan's wisdom, gathered through centuries of experience, will come in remarkably handy, as will his magical abilities, which allow him to hold his own in combat against Jason's enemies.
Pan is above all things a storyteller, and mainly enjoys the voyage as a legendary undertaking that will make for a great story, though he tends to agree with Jason most when he is taking the compassionate route in any given scenario, as that is the way of Apollo.