Andrew brought to the Messiah Simon Peter on whom the church will be built

John 1:40–42 (NIVUK)

40 Andrew, Simon Peter’s brother, was one of the two who heard what John had said and who had followed Jesus. 41 The first thing Andrew did was to find his brother Simon and tell him, ‘We have found the Messiah’ (that is, the Christ). 42 And he brought him to Jesus.
Jesus looked at him and said, ‘You are Simon son of John. You will be called Cephas’ (which, when translated, is Peter).

I. Andrew recognised Jesus as the Messiah (40-41)
Andrew was one of two disciples of the Baptist John, who followed Jesus in v37. They called Jesus ‘Rabbi’ in v38, which means ‘Teacher’. In v41, Andrew calls Jesus ‘the Messiah’ that is ‘the Christ’ in Greek. The Messiah means literally ‘the Anointed One’, and is ‘the Saviour’. Jesus promised in v39, “you will see”. They not only saw where He was staying but also recognised Him as the Messiah.

II. Andrew brought Simon Peter to the Messiah (41-42)
First, Andrew brought his brother Simon to Jesus (41-42). Simon followed Andrew to come to Jesus. Jesus looked at him and identified him(42a). Jesus gave him the vision for a new name, ‘Cephas’ (42b). ‘Cephas’ is ‘Peter’ in Greek and means ‘Rock’. That is, Jesus knew (Exodus 33:12) him, and called him by name (John 10:3, Isaiah 43:1, Isaiah 45:3-4). ‘Calling by name’ in Isaiah 43:1 means God’s special choice of Israel [1]. Note that God also changed Abram to Abraham (Genesis 17:5), Sarai to Sarah (Genesis 17:15), and Jacob to Israel (Genesis 32:28).

III. On this rock, I will build my church (Matthew 16:18)
Simon was given the name Peter in Matthew 16:18. Let us read Matthew 16:15-20 which includes the context.

15 ‘But what about you?’ he asked. ‘Who do you say I am?’
16 Simon Peter answered, ‘You are the Messiah, the Son of the living God.’
17 Jesus replied, ‘Blessed are you, Simon son of Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven. 18 And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it. 19 I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.’ 20 Then he ordered his disciples not to tell anyone that he was the Messiah.

After Simon confessed his faith (Matthew 16:16), Jesus called him Peter (Rock), on that He would build His church (Matthew 16:18).

References
[1] Barry, John D. et al. Faithlife Study Bible.