8:1 Lord … Lord. Of these twin nouns of direct address to God, the first is His specially revealed name Yahweh (Ex 3:14) and the second puts an emphasis on His sovereignty. Your name. The name of God refers to the revealed Person of God, encompassing all of His attributes.
MacArthur Study Bible
8:1 The covenant name (Lord) was given specifically to Israel, but it is majestic … in all the earth, even if not all people acknowledge it.
ESV Study Bible
8:1 Yahweh, our Lord The first Hebrew word used here, yhwh, is God’s personal covenant name to Israel, Yahweh (see note on Exod 3:14). The second Hebrew word, adon, conveys the sense of “master.” This statement declares that Yahweh is the master or ruler over the psalmist and God’s people.
in all the earth Yahweh is the personal God of Israel, and the majesty of His name is known throughout the entire earth.
put your splendor above the heavens This Hebrew phrase used here could indicate that the heavens are the place where God in His glory dwells or that the heavens celebrate God’s glory. It seems that both options appear elsewhere (Pss 19:1; 113:4).
Faithlife Study Bible
8:1 Lord. The personal, or covenantal, name of God revealed to Moses at the burning bush (Ex. 3).
our Lord. A title, which can also be translated “governor” or “master.” He is our Lord because He has established His covenant with His people.
how majestic is your name. The repetition of this line at the end enhances the high note of reverence that pervades the psalm. “Name” signifies the character or reputation of God.
Reformation Study Bible