Let them praise the name of the LORD: for his name alone is excellent; his glory is above the earth and heaven.

for his name alone is exalted.

Let them praise the name of Jehovah: for his name alone is exalted; his majesty is above the earth and the heavens.

They praise the name of Jehovah, For His name alone hath been set on high, His honour is above earth and heavens.

Let them give glory to the name of the Lord: for his name only is to be praised: his kingdom is over the earth and the heaven.

Let them praise the name of the Lord - Let them praise Yahweh - the name being often put for the person.
For his name alone is excellent - Margin, as in Hebrew, exalted. He only is exalted as God. See the notes at Psalm 8:1 : "O Lord, our Lord, how excellent is thy name in all the earth!"
His glory is above the earth and heaven - Compare the notes at Psalm 113:4 : "The Lord is high above all nations, and his glory above the heavens." See also the notes at Psalm 8:1 : "Who hast set thy glory above the heavens."

Let them - All already specified, praise the name of Jehovah, because he excels all beings: and his glory, as seen in creating, preserving, and governing all things, is על al, upon or over, the earth and heaven. All space and place, as well as the beings found in them, show forth the manifold wisdom and goodness of God.

Let them praise the name of the Lord, His nature and perfections, and celebrate the glory of them; and his wonderful works, and the blessings of his goodness, both of providence and grace; even all the above creatures and things, celestial and terrestrial, for the following reasons;
for his name alone is excellent; the name of the Lord is himself, who is excellent in power, wisdom, goodness, truth, and faithfulness, and in all other perfections of his nature; his works, by which he is known, are excellent, both of nature and of grace, and proclaim his glory; his Son, in whom his name is, and by whom he has manifested himself, is excellent as the cedars; and so are all his precious names by which he is called; and such is the Gospel, by which he is notified to the world: nay, the Lord's name is alone excellent; all creature excellencies are nothing in comparison of him, in heaven or in earth, those of angels and men; and therefore should be praised by all, and above all;
his glory is above the earth and heaven; there is the glory of celestial and terrestrial bodies, which differ; the glory of the sun, moon, and stars, and of one star from another; but the glory of the divine Being, the Creator of them, infinitely exceeds the glory of them all: his glorious Majesty resides above heaven and earth; the heaven is the throne be sits upon, and the earth the footstool he stands on; and Christ, who is sometimes called his glory, and is the brightness of it, Psalm 63:2; is exalted above every name on earth, and is made higher than the heavens, and so is exalted above all blessing and praise; see Psalm 8:1.

Let them--all mentioned.
excellent--or, exalted (Isaiah 12:4).
his glory--majesty (Psalm 45:3).
above the earth and heaven--Their united splendors fail to match His.

Above - Above all the glories which are in earth and in heaven.