The Lord Jesus teaches us to put God and His glory first in our prayers.
The phrase ‘Hallowed be Your Name’ in the Lord’s Prayer has many important meanings. It has the emphasis: ‘Your Name must be glorified.’ As Christians, we are to strive to glorify God in everything we do and this is a prayer that we may do so. We are also praying that God would glorify himself in all His dealings with His creation, including the salvation of His people and the condemnation of those who will not turn from their sins.
In short, this is a prayer that is very wide-reaching in its scope but very focused in its objective - the glory of our God.