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 Psalms 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 Psalms 113:4 : “The Lord is high above all nations, and his glory above the heavens.” See also the notes at Psalms 8:1 : “Who hast set thy glory above the heavens.”