What does Alexander mean?
From Greek 'alexein' (to defend, protect) and 'aner/andros' (man), so 'defender/protector of men'. Note this is strictly 'defender' rather than 'warrior', though its martial fame comes from Alexander the Great.
What does George mean?
George comes from the Greek Georgios, “farmer” or “earth-worker,” from gē (“earth”) and ergon (“work”). St George, the dragon-slayer, is the patron saint of England.