What does Mateo mean?
The Spanish form of Matthew, from the Hebrew Mattityahu, meaning 'gift of Yahweh' (mattan 'gift' + Yah, a name of God). It reached Spanish through the Greek Matthaios and Latin Matthaeus, the name of the apostle and gospel-writer.
What does Santiago mean?
A contraction of 'Sant Yago' — Saint James. Yago (also Iago) is the old Spanish form of Jacobo/James, from the Hebrew Ya'aqov (Jacob). The name honors Santiago the Apostle, patron saint of Spain, whose shrine is at Santiago de Compostela.