This is more than a mere formula of praise. How can the name of God be “hallowed”? Actually, the sense of the word might better be expressed in English by “sanctify.” The whole phrase could be translated, “May your name be sanctified.”
Sanctity of God
The sanctity of God is a well-known biblical theme (e.g., Isa. 6:3) and seems to be related to God’s justice. Compare Ezekiel 38:23:
I will show my greatness and my holiness and make myself known in the sight of many nations. Then they will know that I am the LORD.
יתקדש (yit·ka·DESH, “be hallowed” or “be sanctified”), the Hebrew word Jesus probably used in the prayer he taught his disciples, is parallel to והתקדשתי (ve·hit·ka·dish·TI, “I will show…my holiness”) in Ezekiel 38:23. This verse from Ezekiel formed the basis for a number of ancient Jewish prayers. One of these is that of Rabbi Ezekiel which appears in Ta’anit 64b in the Jerusalem Talmud. When the much-needed rains came, he would bless the LORD: “May your name be magnified, sanctified and exalted, our King, for every drop that you send us.”