By faith in his Name hath this for his Name through.faith in his Name, A.V.: the order of the words is changed from that of the A.V., to bring it into accordance with the order of the Greek, but with a great loss of force in English; behold for see, A.
V.; through for by, A.V. Yea, the faith; rather, and the faith. The two propositions are not the same. The first affirms that it is the Name of Jesus which has given him strength, objectively; the second that the faith (subjective) which is through or by him hath given him perfect soundness.
There is some obscurity in the exact meaning of ἡ πίστις ἡ δι αὐτοῦ. Some (see Alford, 1.1) compare 1 Peter 1:21, and make God the object of the faith of his witnesses, Peter and John. Others (Meyer) understand that the faith in the Name of Christ was wrought in Peter and John by or through Christ's ministry and resurrection.
But it is much more consonant with other passages (Acts 14:9; Acts 16:31, etc.; Matthew, Matthew 15:28, etc.) to understand the faith to be that of the man who was healed; and then the phrase, "which is through him," will denote naturally that it was through Jesus Christ that the man's faith brought him into contact, so to speak, with God who healed him.
In the same spirit we read that the lame man "praised God" (verses 8, 9) for the cure effected through the Name of Jesus Christ; and Peter says (verse 15), "Whom God raised from the dead." The interpretation of the phrase ἡ δι αὐτοῦ depends upon whether we supply an active or a passive word.
The faith which acts, or works, or moves through him is one way of understanding it; the faith which is wrought or produced through him is the other. The first is preferable. This perfect soundness; pointing to what they saw with their own eyes while the man was leaping and dancing before them ( ὁλοκληρία, perfect soundness, used only here in the New Testament; it is a medical term).