Q: What do we pray for in the first petition?
A: In the first petition (which is, Hallowed be thy name) we pray, That God would enable us and others to glorify him in all that whereby he maketh himself known, and that he would dispose all things to his own glory.

Psalm 67:1-3. God be merciful unto us, and bless us; and cause his face to shine upon us; Selah. That thy way may be known upon earth, thy saving health among all nations. Let the people praise thee, O God; let all the people praise thee.
2 Thessalonians 3:1. Finally, brethren, pray for us, that the word of the Lord may have free course, and be glorified, even as it is with you.
Psalm 145.
Isaiah 64:1-2. Oh that thou wouldest rend the heavens, that thou wouldest come down, that the mountains might flow down at thy presence, as when the melting fire burneth, the fire causeth the waters to boil, to make thy name known to thine adversaries, that the nations may tremble at thy presence!
Romans 11:36. For of him, and through him, and to him, are all things: to whom be glory for ever. Amen.

Westminster Project - See Matthew Henry's Scripture Catechism based on the WSC to see the theme of the hallowing of God's name all throught the Holy Text.