Peter uses this phrase to emphasize that it is by the authority of Jesus that the man can be told to walk. It is not the use of the phrase in the name of Jesus Christ of Nazareth
that brings healing as if it is a magical incantation. That is to say, Jesus Christ of Nazareth is the one who has power to bring healing. With the apostles serving as his witnesses and representatives (Acts 1:8),1 any miracles that are done through them should be attributed to Jesus Christ.2
6 But Peter said, “I have no silver and gold, but what I do have I give to you. In the name of Jesus Christ of Nazareth, rise up and walk!”