Hebrews 12:1 (KJV)
Wherefore seeing we also are compassed about with so great a cloud of witnesses, let us lay aside every weight, and the sin which doth so easily beset us, and let us run with patience the race that is set before us.
Then spake the Lord to Paul in the night by a vision, Be not afraid, but speak, and hold not thy peace: For I am with thee, and no man shall set on thee to hurt thee: for I have much people in this city.
Acts 18:9-10
Wherefore seeing we also are compassed about with so great a cloud of witnesses, let us lay aside every weight, and the sin which doth so easily beset us, and let us run with patience the race that is set before us.
Then spake the Lord to Paul in the night by a vision, Be not afraid, but speak, and hold not thy peace: For I am with thee, and no man shall set on thee to hurt thee: for I have much people in this city.
Acts 18:9-10

God the Father revealed Jesus' identity to Peter.The name Christian came later. Plus, he knew what his mission was, just as Paul knew....well after the road to Damascus.
Many Jewish people have accepted Jesus as their Saviour over the centuries and I say PRAISE THE LORD. From Jesus' mouth, tells Peter that he is the rock upon which the 'church would be built.' Now remember that Peter was the rock, but Jesus is the cornerstone.