“Hallow” (hagiazo) has the basic meaning of “to separate.” It pictures one thing separated from another or many things into groups. For instance, when growers reap their crops—say, apples—they divide the produce into various categories according to size and quality. Workers segregate the usable but less attractive apples for crushing into applesauce while packaging the high-quality fruit for sale at grocery stores.

A similar idea is present in hallowing or sanctifying something: The best is put in its own category and treated with greater care. In the case of God, people are to put Him in His own exalted category, in which He has no rivals. As He says of Himself in Isaiah 46:9, “For I am God, and there is no other; I am God, and there is none like Me.”

The apostle Paul declares in Ephesians 3:14-15 that “the whole family in heaven and earth is named” from the Father, meaning that He is the ultimate Ruler over all things. Further, “God has highly exalted [Jesus Christ] and given Him the name which is above every name” (Philippians 2:9). These facts should establish that His excellent name is truly the highest in all the universe, and He is due all praise and honor and obedience for His sovereign position over all things in heaven and earth.

The proper response of His people, then, is to come to a true understanding of God and learn to follow His teachings, as He prophesies Israel will do once He gives them His Spirit in the age to come. The elect are currently experiencing this process in this age, absorbing His teaching and through many trials figuring out how to practice His ways, continually keeping Him in the center of their lives. They hallow His name in their praise of Him and in their obedience to Him in every word and deed.

In the end, “Hallowed be Your name” expresses the supplicant's desire to please the Father in every facet of life and witness His glory to the world.