Pheonix

I think that the author chose the name Pheonix because it a bird that "never dies" and that probably means when "Pheonix goes into the game" he won't die. The pheoix (bird) is said to have gone up in flames once it's baby has been born. There can only be one pheonix at a time. On the third day the pheonix rises from the ashes, or flames, and the baby gathers the ashes and takes them to the altar of the sun god, Re.

In the Shadow of the Minotaur I think Alan Gibbon named his main character Pheonix because maybe he is follow in his parents or relatives footsteps. The bird rises from the dead. Maybe Pheonix is the "rise from the dead" of his uncle.