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 Diego mean?
A Spanish name of genuinely disputed origin. Traditionally explained as a short form of Santiago (Sant-Yago, 'Saint James', from Hebrew Jacob), but many scholars now derive it instead from the Latin Didacus — itself possibly from the Greek didache 'teaching'. The two theories remain unresolved, so any single 'meaning' should be treated with caution.