From the commentary King Comments (Psalm 20):
Three times in this psalm the remnant appeals to “the name” (Psa 20:1b; 5; 7). Here is the first time. That God is “the God of Jacob” indicates that He will fulfill all the promises He has made to Jacob, despite the many times Jacob has been unfaithful. This is a great encouragement to the remnant who are also aware of their own unfaithfulness. It is also a great encouragement to us, who are also so often unfaithful, that God will fulfill all His promises. The place on high gives the assurance that no one can make His king or anyone of His own miss the fulfillment of His promises.