God's name is kept holy when the Word of God is taught in its truth and purity, and we, as the children of God, also lead holy lives according to it. Help us to do this, dear Father in heaven! (Small Catechism: Lord's Prayer, First Petition)
In the Name + of Jesus. Amen. That Name is holy by itself. Jesus doesn't need our prayers to make it holy. But that He provides this petition for us to pray implies that His Name can be profaned.
To be holy is to be set apart, unique. To be profane is to be common--not necessarily bad, just common. The Name of God is a holy Name because, unlike other names, God's Name is more than a mere identifier. God's Name is what stands behind God's Word. Anytime His Word is taught, His Name is on the line. And when that Word is taught rightly, His Name is kept holy.
God's Name also has a special place in life, too. It is the Name that turns Baptism from plain water to a lavish washing away of sin. The Name of God is in the water, and everyone washed with that water receives the Name. You are marked as His own. And so His Name also stands behind you. When you do or say something as a Christian, it's also Christ's Name on the line.
Left to our own devices, we would treat God's Name with more profanity than a drunken sailor. There is no power in us to do what God expects us to do in the Second Commandment, that is, to use His Name rightly. That's why He gives us this petition to pray.
The only way that God's Name can be used rightly, the only way it is kept holy, is if God is the One who accomplishes it. "Help us to do this, dear Father in heaven!" This is what is so unique, so holy about God's Name--whenever you call upon it, it accomplishes every promise attached to it! In the Name + of Jesus. Amen.
Your name be hallowed. Help us, Lord, In purity to keep Your Word,
That to the glory of Your name We walk before You free from blame.
Let no false teaching us pervert; All poor deluded souls convert. (Our Father, Who from Heaven Above, LSB 766:2)