“our lord.” The Hebrew for “lord” is a grammatical plural, Adonainu, a title also used of David (1 Kings 1:43, 47). The “grammatical plural” is often referred to by scholars as a “plural of majesty,” a “plural of emphasis,” or a “plural of excellence,” because the plural adds emphasis and/or majesty to an individual, it is not a plural of number, as if there was more than one individual being referred to.
“how majestic is your name in all the earth.” Psalm 8 is one of the psalms that is all praise. There are nine verses, and none of them are asking for anything in prayer or recounting biblical history; the whole psalm is about the greatness of God and what He has done. There are a number of psalms that are like Psalm 8 in that they focus almost exclusively on praise: Psalm 8, 19, 23, 33, 47, 67, 84, 93, 96, 100, 111, 113, 117, 150. One of the great values in these psalms is that reading them over and over helps us with our personal praise of God. Modern culture does not praise a lot, or for that matter even say “Thank you” very much, and so reading and reciting praise psalms helps people understand and vocalize praise.