After addressing our prayers unto "our Father in heaven," Jesus says our Father's name is to be "hallowed" (Matt. 6:9; Luke 11:2). The word "hallow" means to regard as holy, to honor as sacred, or to give due reverence and respect unto someone or something. It is translated from the Greek word hagiazo, which means to render or acknowledge to be sacred or holy.
Our Father in heaven is separate from all sin and above every common thing. Our prayers should acknowledge this fact in words of praise. Brother Paul Earnhart has made the following comments regarding the hallowing of God's name in our prayers: "To hallow the name of God means simply to hold Him in reverence to place Him in that special high and holy place where He belongs as the God of all creation and the Father of our Lord Jesus Christ. Of course, He is already the holy God, and there is no means at our command to make Him holier. The concern of this petition is that men everywhere should acknowledge in their own hearts and lives what is manifestly true... So our prayers are to begin, not with a concern for ourselves, but with a concern for the honor of our Father" ("Invitation to a Spiritual Revolution," page 86).
The nation of Judah profaned God's name throughout the world when they rejected the Lord in favor of idolatry (Ezek. 36:16-38). God had punished them and cleansed them with the Babylonian captivity. When the nations saw Judah returned to their land and serving the Lord with a loyal heart, then God would be "hallowed in you before their eyes" (v. 23).
Praying "Hallowed be Thy name" is more than praising the high and holy name of God. It is an acknowledgement that we have a responsibility to live in such a way that will cause God's name to be "hallowed" by the world.