Why does Paul call Peter "Cephas" in his writings?

In John 1:42 Jesus called Peter as Cephas. > Jesus looked at him and said, “You are Simon son of John. You will be called Cephas” (which, when translated, is Peter). But throughout the Gospels, Peter was called as Peter and his books also called in his name I Peter and II Peter. But why did Paul call Peter, Cephas (Galatians 2:7-14, I Cor. 1:11-13, I Cor. 3:21, I Cor. 9:5 and I Cor. 15:5)? In some occasions he also calls him as Peter. When I asked my mom, she said Paul was rebuking Peter in the name Cephas. Is this true? Or is calling Peter as Cephas normal? At times, Paul and Peter had disagreements as in Galatians 2:11-16: > 11 When Cephas came to Antioch, I opposed him to his face, because he stood condemned. 12 For before certain men came from James, he used to eat with the Gentiles. But when they arrived, he began to draw back and separate himself from the Gentiles because he was afraid of those who belonged to the circumcision group. 13 The other Jews joined him in his hypocrisy, so that by their hypocrisy even Barnabas was led astray. 14 When I saw that they were not acting in line with the truth of the gospel, I said to Cephas in front of them all, “You are a Jew, yet you live like a Gentile and not like a Jew. How is it, then, that you force Gentiles to follow Jewish customs? > 15 “We who are Jews by birth and not sinful Gentiles 16 know that a person is not justified by the works of the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by the works of the law, because by the works of the law no one will be justified. How was their relationship as fellow apostles?