The New Testament identifies Simon Bar Jonah as Peter the majority of times he is mentioned in the text. Jesus only did so four times; once when He first met Peter, again when He revealed Peter's high purpose, and a third time when He warned him of his impending failure. Every other time Jesus called him Simon or Simon bar Jonah. I find the DNA of God's kindness and mercy embedded in the times Jesus chose to address his beloved friend as Peter. The first time the two of them met, Jesus gave him a new name, an inkling from the very genesis of their relationship that Simon did not yet truly know who he was. The second time Jesus called him Peter He revealed Simon's true identity; a rock worthy of helping to sustain a new kingdom that would eventually rule the world. The third time Jesus addressed him as Peter when He sternly warned him that before dawn he would deny Him with oaths and cursing. That failure could have destroyed him. Jesus used the name Peter then to remind him of his true identity and calling, and that though his failure was imminent so too was his high calling.
A fourth and strategic time Jesus referred to Simon as Peter. After he denied the Lord and Jesus was crucified and resurrected a man in sparkling robes sitting outside the empty tomb relayed this message to the ladies who came there, "But go, tell His disciples — and Peter — that He is going before you into Galilee; there you will see Him, as He said to you" (Mark 16:7). Jesus used the name Peter to remind the fallen apostle of his high calling. Jesus was not through with His beloved fisherman. When He first warned Peter of his denial He also said, "But I have prayed for you, that your faith should not fail; and when you have returned to Me, strengthen your brethren" (Luke 22:32).
I am sure Peter didn't understand all that as it happened but I bet it made a lot of sense to him later as he struggled with his calling and his failure. Jesus promised all of us that He would never leave us nor forsake us. He was with Peter the whole way in more ways than he could readily understand. Take heart. He is with us as well.