In what power They do yet seem to have some zeal of God. For they feign that they are careful that the honor due unto God may not be given to any other. Name is taken in this place for authority. In sum, they deal as if they were most earnest defenders and maintainers of God's glory. In the mean season, their importunateness is wonderful, in that they go about to drive the apostles to make denial, by asking many questions concerning a manifest matter, and to wring out by fear some other thing than they had confessed. But God doth bring their crafty wiliness to nought, and maketh them hear that which they would not.

In the midst - In the presence of the Great Council.
By what power - A similar question was put to Christ in the temple, Matthew 21:23.
By what name - That is, by whose authority. It is very probable that they expected to intimidate the apostles by this question. They claimed the right of regulating the religious affairs of the nation. They had vast power with the people. They assumed that all power to instruct the people should originate with them; and they expected that the apostles would be confounded, as having violated the established usage of the nation. It did not seem to occur to them to enter into an investigation of the question whether this acknowledged miracle did not prove that they were sent by God, but they assumed that they were impostors, and attempted to silence them by authority. It has been usual with the enemies of religion to attempt to intimidate its friends, and when argument fails, to attempt to silence Christians by appealing to their fears.

By what power, or by what name, have ye done this? - It seems that this council were convinced that the lame man was miraculously healed; but it is very likely that they believed the whole to be the effect of magic; and, as all intercourse with familiar spirits, and all spells, charms, etc., were unlawful, they probably hoped that, on the examination, this business would come out, and that then these disturbers of their peace would be put to death. Hence they inquired by what power, εν ποιᾳ δυναμει, by what supernatural energy; or in what name, by what mode of incantation; and who is the spirit you invoke, in order to do these things? False prophets, reputed witches, wizards, etc., were to be brought before the sanhedrin, to be by them judged, acquitted, or condemned, according to the evidence. Some think the words should be thus understood: Who gave you authority to teach publicly! This belongs to the sanhedrin. What, therefore, is your authority, and who is he who gave it to you?

(2) And when they had set them in the midst, they asked, By what power, or by what (e) name, have ye done this?
(2) Against those who brag of a succession of persons, without a succession of doctrine, and by that means beat down the true ministers of the word, as much as they are able.
(e) By what authority.

And when they had set them in the midst,.... Of the assembly, as the Ethiopic version adds; in the middle of the sanhedrim, which sat in a semicircular form; or as the Jews express it, as the half of a round corn floor, or as a half moon, and not in a perfect circle; because it was necessary that the contending parties, and the witnesses, might go in and speak before them all (b); so that those that were set before them, were placed in the middle of them: and here Peter and John were set; so the Arabic version renders it, "when they set both": they sent for them out of the hold, or custody, where they had been all night, and ordered them to be brought before them, to be examined about their doctrine and practice:
they asked, by what power, or by what name have ye done this? they inquired of them, whether it was by a natural, or by a divine, or by a diabolical power, that they had wrought the cure upon the lame man? whether it was by the use of medicine, or by the help of magic art, and the assistance of the devil, which they were very ready to charge Christ and his disciples with? or whether they pretended to a divine and supernatural aid? and also what name they had made use of, and by whose authority they acted?
(b) Misn. Sanhedrin, c. 4. sect. 3. & Bartenora in ib.

By what power or . . . name have ye done this--thus admitting the reality of the miracle, which afterwards they confess themselves unable to deny (Acts 4:16).

Set them in the midst. The high priest acted as president, and the members were arranged in a semi-circle around him, with the prisoners in front.
By what power? They could not deny the miracle, but they thought that it had been done by some incantation. They ask an explanation.

By what name - By what authority, have ye done this? - They seem to speak ambiguously on purpose.