In "Biblical Perspective" Gordon Snider writes:
David called for God to exert His power against David's enemies not only because of the rightness of his case, but also in judgment of their evil deeds. (The Hebrew grammar here allows us to understand verses 5 and 6 either as a request for God's action or that David was so sure that God would answer his prayer that he put the verbs in past tense although the event was still future.) In effect, David was saying, “Act in defense of your great name, as well as for my benefit.” Put out their name for ever.
Source: Studies in the Psalms: Adult Teacher's Insights, page 5.