The Greek verb diaggello means to proclaim, to announce thoroughly, or to spread news throughout a region. The prefix dia- intensifies the verb aggello (to announce), conveying the idea of proclamation that penetrates everywhere.
Diaggello is used for the widespread proclamation of the gospel — an announcement that travels through and across every boundary. In Romans 9:17, God's purpose in Pharaoh was that His name be diaggello throughout the earth, showing that even hardened opposition serves the spread of God's renown.
Theologically, diaggello reminds believers that the gospel cannot be contained — it is meant to spread through every corner of creation. God's purposes in history are never frustrated; even resistance becomes a vehicle for proclamation.