O Lord - Hebrew, יהוה Yahweh. It is an address to God by his chosen and special title, Exodus 3:14. Compare the notes at Isaiah 1:2.
Our Lord - The word used here - אדני 'âdônay - means properly master, lord, ruler, owner, and is such a title as is given to an owner of land or of slaves, to kings, or to rulers, and is applied to God as being the ruler or governor of the universe. The meaning here is, that the psalmist acknowledged Yahweh to be the rightful ruler, king, or master of himself and of all others. He comes before him with the feeling that Yahweh is the universal ruler - the king and proprietor of all things.
How excellent is thy name - How excellent or exalted art thou - the name being often used to denote the person. The idea is,” How glorious art thou in thy manifested excellence or character.”
In all the earth - In all parts of the world. That is, the manifestation of his perfect character was not confined to any one country, but was seen in all lands, and among all people. In every place his true character was made known through His works; in every land there were evidences of his wisdom, his greatness, his goodness, his condescension.
Who hast set thy glory above the heavens - The word used here, and rendered “hast set,” is in the imperative mood - תנה tenâh - give; and it should probably have been so rendered here, “which thy glory give thou;” that is, “which glory of thine, or implied in thy name, give or place above the heavens.” In other words, let it he exalted in the highest degree, and to the highest place, even above the heavens on which he was gazing, and which were in themselves so grand, Psalms 8:3. It expresses the wish or prayer of the writer that the name or praise of God, so manifest in the earth, might be exalted in the highest possible degree - be more elevated than the moon and the stars - exalted and adored in all worlds. In His name there was such intrinsic grandeur that he desired that it might be regarded as the highest object in the universe, and might blaze forth above all worlds. On the grammatical construction of this word - תנה tenâh - see an article by Prof. Stuart, in the Bibliotheca Sacra, vol. ix. pp. 73-77. Prof. Stuart supposes that the word is not formed from נתן nâthan - to give, as is the common explanation, but from תנה tânâh - to give presents, to distribute gifts, Hosea 8:9-10, and that it should be rendered, Thou who diffusest abroad thy glory over the heavens.