Peter wants to make it very clear to which Jesus he is referring. He is talking about Jesus of Nazareth, the one who claimed to be the Christ and was put to death by the Jewish authorities. Since the death of Jesus took place only a few months ago at that time, the council will know exactly who he is talking about and also remember some of the claims which Jesus made.
10 let it be known to all of you and to all the people of Israel that by the name of Jesus Christ of Nazareth, whom you crucified, whom God raised from the dead by him this man is standing before you well.