I have for a long time associated Peregrinus's, and Polycarp's, desire to die by fire as a way to embody the Logos.
The question is, was Peregrinus still a Christian when he died? Lucian separates his time with the Christians and his time as a Cynic as two distinct periods. But, I have felt that Lucian saying that he fell in with the Christians is anachronistic, and that Peregrinus actually joined a Jewish sectarian community somewhere in the Syrian/Palestine region.
So, could Peregrinus have been using common Gentile terms and names of gods, as synonymous with Christ?
Hercules then equates to Jesus, and Justin Martyr did make a comparison between Hercules and Jesus:
And when they tell that Hercules was strong, and travelled over all the world, and was begotten by Jove of Alcmene, and ascended to heaven when he died, do I not perceive that the Scripture which speaks of Christ, 'strong as a giant to run his race,' has been in like manner imitated?
What's more, Hercules was the hero of athletes, and being an
ahlete of Christ is encouraged in certain texts.
Epistle of Ignatius to Polycarp:
Speak to every man separately, as God enables you. Bear the infirmities of all, as being a perfect athlete [in the Christian life]: where the labour is great, the gain is all the more.
Be sober as an athlete of God: the prize set before you is immortality and eternal life, of which you are also persuaded. In all things may my soul be for yours, and my bonds also, which you have loved.
It is the part of a noble athlete to be wounded, and yet to conquer.
But then, what of Proteus?
Proteus was a god who could change his shape and form at will. This reminds of the notion of transmigration, or the Christ jumping from one host to another. Thus Christ is able to change its own form, so to speak, when he appears in different bodies.
And the Phoenix? That one's easy. The Phoenix was the symbol of resurrection in the ancient world. It would make a nest and die amidst its flames. But out of its ashes, a new Phoenix bird would be born--but really, the old one would be
reborn.
Peregrinus, adopting hi new and last name for himself as Phoenix, would also wish for a resurrection.