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 Theodore mean?
From Greek Theodoros, combining theos 'God' and doron 'gift' — literally 'gift of God'. Note that Theodore and Dorothea are built from the SAME two elements in reversed order.