Acts 4:5 On the next day, their rulers and elders and scribes were gathered together in Jerusalem; 6 and Annas the high priest was there, and Caiaphas and John and Alexander, and all who were of high-priestly descent. 7 When they had placed them in the center, they began to inquire,
“By what power, or in what name, have you done this?” 8 Then Peter, filled with the Holy Spirit, said to them, “Rulers and elders of the people, 9 if we are on trial today for a benefit done to a sick man, as to how this man has been made well, 10 let it be known to all of you and to all the people of Israel, that
by the name of Jesus Christ the Nazarene, whom you crucified, whom God raised from the dead—
by this name this man stands here before you in good health. 11
He is the stone which was rejected by you, the builders, but which became the chief corner stone.
12 And there is salvation in no one else; for there is no other name under heaven that has been given among men by which we must be saved.”
In bold for emphasis. There is no change. The context is clear. The Person, Jesus Christ, is the same subject throughout. There is no superstitious belief in repeating His name that is the concern here. The rulers/judges asked Peter "by what power or name" this miracle was done? He answered their question directly and truthfully. "by the name of Jesus Christ the Nazarene".
Neither is there salvation in any other,.... Meaning not corporeal healing, but spiritual and eternal salvation; the Syriac version renders it, neither is there "redemption in any other": Christ is the only Saviour and Redeemer, who was promised and prophesied of as such; who has saved and redeemed his people from the law, sin, and Satan; nor is salvation to be sought and hoped for from any other; not in a man's self, nor in any other creature, angels or men; not in and by his own works, and legal righteousness; not by obedience to the law of Moses, moral or ceremonial; nor by the light of nature, much less by an observance of the traditions of the elders:
for there is none other name; thing or person, be it ever so great, or whatever show of power and strength, of holiness and religion, it makes; as the name of kings, princes, and the great men in the world; or of ministers and preachers in the church; or even of Christians and believers, which may be only a name to live; none but the name of Jesus, his person, blood, and righteousness:
under heaven: throughout the whole earth, in all the nations and kingdoms of it; nor even in heaven itself, among all the mighty angels there, thrones, dominions, principalities, and powers; none but the Father and the Spirit, who are one with Christ: there is none but he
given among men; and he has been freely given by his Father, as an instance of his matchless love to the world; and also freely given by himself, to be a sacrifice for the sins of his people; and is freely preached among men, as the only Saviour of them; for there is no other,
whereby we must be saved: God resolved in his purposes and decrees, in his council and covenant, upon the salvation of his chosen people; and he appointed his Son to be the salvation of them, and determined he would save them by him, and by no other, and in no other way; wherefore, whoever are saved, must be saved by him, see
Hosea 1:7 the Arabic version adds, "unless by him only". Gill's Exposition of the Entire Bible