What does Matthew mean?
English form of the Hebrew name Mattityahu (Mattathias), from mattath 'gift' + yah, a short form of the divine name Yahweh. The structure is 'gift of God': 'gift' + the name of God.
What does Joseph mean?
Joseph comes from the Hebrew Yosef, “he will add” or “God will increase.” It is borne by Joseph of the coat of many colours and by St Joseph, husband of Mary.