English Standard Version (ESV)
35 The next day again John was standing with two of his disciples, 36 and he looked at Jesus as he walked by and said, “Behold, the Lamb of God!” 37 The two disciples heard him say this, and they followed Jesus. 38 Jesus turned and saw them following and said to them, “What are you seeking?”And they said to him, “Rabbi” (which means Teacher), “where are you staying?” 39 He said to them,“Come and you will see.” So they came and saw where he was staying, and they stayed with him that day, for it was about the tenth hour. 40 One of the two who heard John speak and followed Jesus was Andrew, Simon Peter's brother. 41 He first found his own brother Simon and said to him, “We have found the Messiah” (which means Christ). 42 He brought him to Jesus. Jesus looked at him and said, “You are Simon the son of John. You shall be called Cephas” (which means Peter).
John was with two of his disciples, one of whom was Peter's brother Andrew. John proclaimed Jesus to be the Lamb of God as he walked by, and they followed Him. Jesus noticed and questioned them, saying something along the lines of "What are you looking for?" They returned by questioning where Jesus was staying. Jesus invited them to come and see. Then they stayed with Him for that day. In this short amount of time, whether by John's proclamation or by being with Jesus or both, Andrew became convinced of the fact that Jesus was the Messiah. So he went and told his brother, and brought him to Jesus. Jesus looked at Peter (who at that time was called Simon) and said he shall be called Peter.
Thought for the Day: What would you think if someone met you and immediately decided that you should be called by another name? Was this like being called by a nickname, which many wear as a badge of honor, or was it like taking away his given name and changing it, which many would find offensive? Apparently, Peter did not find it offensive, as we know that he followed Jesus from that point forward. So what name would Jesus have for me if he were to meet me today?