Albert Barnes Commentary Psalms 54:1

"Save me, O God, by thy name, And judge me in thy might." — Psalms 54:1 (ASV)

Save me, O God, by thy name - The word “name” here may include the perfections or attributes properly implied in the name. It is a calling on God as God, or in view of all that is implied in his name, or that constitutes the idea of “God.” That name would imply all of power and benevolence that was necessary to secure his salvation or safety.

The particular object of the prayer here is that God would save him from the design of the Ziphims to betray him to Saul. In some way David seems to have been apprised of the information which they had given to Saul, or at least to have suspected it so strongly that he felt it was necessary for him to move from place to place in order to find safety.

And judge me by thy strength - The word “judge” here is used in the sense of declaring a judgment in his favor, or of vindicating him. See the notes at Psalm 7:8. Compare Psalm 18:20; Psalms 26:1; Psalms 43:1. The idea is, Vindicate or save me by your power.