Like so many of his Jєωιѕн contemporaries, he was attracted by the Baptist's preaching of penance and was, with his brother Andrew, among John's associates in Bethania on the eastern bank of the Jordan. When, after the High Council had sent envoys for the second time to the Baptist, the latter pointed to Jesus who was passing, saying, "Behold the Lamb of God", Andrew and another disciple followed the Saviour to his residence and remained with Him one day.
Later, meeting his brother Simon, Andrew said "We have found the Messias", and brought him to Jesus, who, looking upon him, said: "Thou art Simon the son of Jona: thou shalt be called Cephas, which is interpreted Peter". Already, at this first meeting, the Saviour foretold the change of Simon's name to Cephas (Kephas; Aramaic Kipha, rock), which is translated Petros (Latin, Petrus) a proof that Christ had already special views with regard to Simon. Later, probably at the time of his definitive call to the Apostolate with the eleven other Apostles, Jesus actually gave Simon the name of Cephas (Petrus), after which he was usually called Peter, especially by Christ on the solemn occasion after Peter's profession of faith (Matthew 16:18; cf. below). The Evangelists often combine the two names, while St. Paul uses the name Cephas.
http://www.newadvent.org/cathen/11744a.htm