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 sachez-le tous, et que tout le peuple d'Israël le sache! C'est par le nom de Jésus-Christ de Nazareth, que vous avez crucifié, et que Dieu a ressuscité des morts, c'est par lui que cet homme se présente en pleine santé devant vous.