What does Theo mean?
Short form of Theodore (or feminine Theodora), from Greek theos 'God' + doron 'gift'. Carries the 'gift of God' sense of the full name; on its own the element theos means 'God'.
What does Phoenix mean?
From Greek 'phoinix', the mythical bird that is consumed by fire and reborn from its own ashes. The fire link is through the rebirth-by-fire myth rather than a literal word for fire.