Duane Garrett proposes the following structure for Psalm 8 in his new Pillar Commentary on the Psalms (p. 118).
The envoi (v. 9) repeats the titular line (v. 1a) verbatim. Some scholars regard the whole of the psalm as a chiasm, but this is not persuasive. Verses 1-2 should be taken together as the introductory words of worship. Verse 2 provides important context to the body of the psalm in vv. 3-8, but it is radically different from those verses and should not be included with that stanza. The psalm is thus in three parts:
A. Opening Praise to God (vv. 1-2)
B. God’s Regard for Humanity (vv. 3-8)
C. Envoi of Praise (v. 9)
The titular line, “YHWH, our Lord, how majestic is your name in all the earth!” immediately indicates that this psalm focuses on praise and not on appeals for help. Verses 1-2 foreshadow the two themes of the psalm. First, God is creator of heaven and earth. Second, despite how puny humans are, God has high regard for them (foreshadowed in the focus on “children and infants” in v. 2). The body of the psalm focuses on how surprising it is that so feeble a creature as humanity should be so exalted within the whole of creation.
Having surveyed the outlines by Waltke, Ross (KEL), and Hamilton (EBTC), Garrett’s outline most commends itself to me.
I’m having a hard time separating 1a and 1b (as Waltke and Ross want to do). The verse seems to hold together. This is especially so in Hebrew, where 1b links to 1a with אֲשֶׁ֥ר. In addition, 1a speaks about a majestic name in the earth while 1b speaks of glory above the heavens.
I further agree with Garrett, that verse 2 combines with verse 1 to set the theme for the psalm. There is a contrast between God’s great majesty and “splendor” (LSB) and man, as represented by “infants and nursing babies” (CSB). And yet verse 2 is foreshadowing the important place God has granted humans: he establishes “a stronghold” (CSB) through the praise of “infants and nursing babies.”
The body of the poem is verses 3–8, and this comes in two parts.
In verses 3–4 David considers the heavens (cf. v. 1) and the glory of that creation causes him to marvel that God is mindful of man, who seems insignificant by comparison (cf. v. 2).
In verses 5–8 David then expands on the exalted position in which God has made man. Verse 5a locates man in relation to the “heavenly beings” (ESV), and man is only a “little lower” than them. Verse 5b notes that God crowned man with “glory and honor.” Verse 6 identifies what that glory and honor consists of: dominion over God’s creation. Verses 7–8 then specify the content of the “all things” over which God has given man dominion.
Verse 9 concludes by repeating 1a, but with verse 1 the majesty of God was in the created things, especially in the heavens. Verse 9 is informed by all the precedes it and thus includes with the majesty of Yhwh’s name his crowning man with glory and honor over the rest of creation.

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