To hallow is to bless or sanctify, to make holy. Hallow can also be to respect and treat as holy, as sacred. To “hallow this ground,” for example, means to respect the place where we bury our dead. When we pray the Our Father, the line that says “hallowed be Thy name” does not mean we are asking God to bless His own name, rather, we are making an emphatic statement that God’s name is holy and should be treated as holy.
The Commandment that forbids us to use the name of the Lord in vain (blasphemy) is implied here, but this goes much further by insisting not only that we don’t take His name in vain, but also that we respect it and treat it as holy. Someone’s name is more than just a word. It is how they are known to others, friend and foe alike. The sacred name of God as revealed to Moses in Exodus was the tetragrammaton; transliterated from the Hebrew, it is YHVH and it is the personal and sacred name of God the Almighty. No one could speak it but the high priest in the Temple of Jerusalem once a year, on the day of Atonement (Yom Kippur), while he stood behind the veil in the sanctuary that preceded the Tabernacle, wherein lay the tablets of stone containing the Ten Commandments.
So sacred was the name that devout Jews to this day do not speak it, instead using the terms Adonai (Lord) or Elohim (God). Nowadays, Christians use the name of God and Jesus to swear and curse with no shame or embarrassment. “Hallowed be Thy name” is something Christians should rediscover. Keeping God’s name, God’s day (Sunday), and God’s will holy is how we “hallow” or sanctify our lives.