Yes, he is still known as Cephas.
a Syriac surname given by Christ to Simon (John 1:42), meaning "rock."
I don't see that is was 'given' at all; but merely proclaiming what will be.
Augustine
Why have I wanted to make this little introduction? In order to suggest to you that in Peter the Church is to be recognized. Christ, you see, built his Church not on a man but on Peter's confession. What is Peter's confession? 'You are the Christ, the Son of the living God.' There's the rock for you, there's the foundation, there's where the Church has been built, which the gates of the underworld cannot conquer. Sermons, Volume III/6, Sermon 229P.1, p. 327.
..ORIGEN'S Commentary (A.D. 186-253),
"If we also say the same as Peter, 'Thou art the Christ, the Son of the living God', not by the instruction of flesh and blood, but by the illumination of the heavenly Father in our hearts, we ourselves become the same thing as Peter.
There was NO indication in scripture that peter was ever views as a pope, or that the "bishop of Rome had any church primacy, there is no evidence in scripture that Peter was ever in Rome..
1Cor. 3:11 it "OTHER foundation can no man lay than that IS LAID, which is JESUS CHRIST".