II. The petitions, and those are six; the three first relating more immediately to God and his honour, the three last to our own concerns, both temporal and spiritual; as in the ten commandments, the four first teach us our duty toward God, and the last six our duty toward our neighbour. The method of this prayer teaches us to seek first the kingdom of God and his righteousness, and then to hope that other things shall be added.

      1. Hallowed be thy name. It is the same word that in other places is translated sanctified. But here the old word hallowed is retained, only because people were used to it in the Lord's prayer. In these words, (1.) We give glory to God; it may be taken not as a petition, but as an adoration; as that, the Lord be magnified, or glorified, for God's holiness is the greatness and glory of all his perfections. We must begin our prayers with praising God, and it is very fit he should be first served, and that we should give glory to God, before we expect to receive mercy and grace from him. Let him have praise of his perfections, and then let us have the benefit of them. (2.) We fix our end, and it is the right end to be aimed at, and ought to be our chief and ultimate end in all our petitions, that God may be glorified; all our other requests must be in subordination to this, and in pursuance of it. "Father, glorify thyself in giving me my daily bread and pardoning my sins," &c. Since all is of him and through him, all must be to him and for him. In prayer our thoughts and affections should be carried out most to the glory of God. The Pharisees made their own name the chief end of their prayers (Mt 6:5, to be seen of men), in opposition to which we are directed to make the name of God our chief end; let all our petitions centre in this and be regulated by it. "Do so and so for me, for the glory of thy name, and as far as is for the glory of it." (3.) We desire and pray that the name of God, that is, God himself, in all that whereby he has made himself known, may be sanctified and glorified both by us and others, and especially by himself. "Father, let thy name be glorified as a Father, and a Father in heaven; glorify thy goodness and thy highness, thy majesty and mercy. Let thy name be sanctified, for it is a holy name; no matter what becomes of our polluted names, but, Lord, what wilt thou do to thy great name?" When we pray that God's name may be glorified, [1.] We make a virtue of necessity; for God will sanctify his own name, whether we desire it or not; I will be exalted among the heathen, Ps 46:10. [2.] We ask for that which we are sure shall be granted; for when our Saviour prayed, Father glorify thy name, it was immediately answered, I have glorified it, and will glorify it again.

Source: Matthew Henry's Commentary on the Whole Bible Volume V (Matthew to John)