Bar-Jonah is a phrase Jesus used when calling Peter in Matthew 16, meaning "son of Jonah."
Matt 16:17Jesus replied, “Blessed are you, Simon Bar-Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven.
In the Gospel of John, Peter's father is named John (Peter's father). Therefore, there is a theory that this Jonah is another name for John (Peter's father).
John 21:15When they had finished eating, Jesus said to Simon Peter, “Simon son of John, do you love me more than these?” “Yes, Lord,” he said, “you know that I love you.” Jesus said, “Feed my lambs.”John 21:16Again Jesus said, “Simon son of John, do you love me?” He answered, “Yes, Lord, you know that I love you.” Jesus said, “Take care of my sheep.”John 21:17The third time he said to him, “Simon son of John, do you love me?” Peter was hurt because Jesus asked him the third time, “Do you love me?” He said, “Lord, you know all things; you know that I love you.” Jesus said, “Feed my sheep.
Another theory suggests that Jesus was referring to Peter's fiery personality, similar to Jonah the prophet, but also symbolizing that Peter, like Jonah, would later repent.