A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
psa 20:1David probably composed this Psalm to express the prayers of the pious for his success as at once the head of the Church and nation. Like other compositions of which David in such relations is the subject, its sentiments have a permanent value--the prosperity of Christ's kingdom being involved, as well as typified, in that of Israel and its king. (Psa 20:1-9)
hear thee--graciously (Psa 4:1).
name of--or manifested perfections, as power, wisdom, &c.
defend thee--set thee on high from danger (Psa 9:9; Psa 18:3).
psa 20:2strengthen thee--sustain in conflict; even physical benefits may be included, as courage for war, &c., as such may proceed from a sense of divine favor, secured in the use of spiritual privileges.
psa 20:3all thy offerings--or gifts, vegetable offerings.
accept--literally, "turn to ashes" (compare Kg1 18:38).
Selah--(See on Psa 3:2).
psa 20:4thy counsel--or plan.
psa 20:5salvation--that wrought and experienced by him.
set up our banners-- (Num 2:3, Num 2:10). In usual sense, or, as some render, "may we be made great."
psa 20:6He speaks as if suddenly assured of a hearing.
his anointed--not only David personally, but as the specially appointed head of His Church.
his holy heaven--or, literally, "the heavens of His holiness," where He resides (Psa 2:6; Psa 11:4).
saving . . . hand--His power which brings salvation.
psa 20:7remember--or cause to remember, mention thankfully (Sa1 17:45; Psa 33:16).
psa 20:8They--that is, who trust in horses, &c.
stand upright--literally, "we have straightened ourselves up from our distress and fears."
psa 20:9let the king hear--as God's representative, delivered to deliver. Perhaps a better sense is, "LORD, save the king; hear us when we call," or pray.