Why do these Greeks approach Philip and Andrew?
It was most likely because they have Greek names .
On the human level, that seems to be the only reason.
Earlier, in Chapter 6, people walked away from Jesus because they could not accept his teaching that he would give his own flesh and blood as the food of eternal life. Then, Simon Peter professed the faith of the disciples, “Master, to whom shall we go? You have the words of eternal life." (6: 68).
Yet, the disciples are still learners.
It was Philip and Andrew who could not see that Jesus could feed the multitude even though they had been with him for some time and had witnessed his power. 
Yet, it is Philip and Andrew who had the privilege of introducing people to Jesus.
It is not up to them, their faith, or their ability. It is because "The hour has come for the Son of Man to be glorified." (v. 23).
So it is with all of Jesus' disciples. It is by God's design and power that we are who we are, messengers and witnesses of the love and power of God.
. Francis J. Moloney, The Gospel of John (Sacra Pagina Series, Volume 4). Collegeville, MN, Liturgical Press, 1998; p. 359.
 When Jesus raised his eyes and saw that a large crowd was coming to him, he said to Philip, “Where can we buy enough food for them to eat?” He said this to test him, because he himself knew what he was going to do. Philip answered him, “Two hundred days’ wages worth of food would not be enough for each of them to have a little [bit].” One of his disciples, Andrew, the brother of Simon Peter, said to him, “There is a boy here who has five barley loaves and two fish; but what good are these for so many?” (John 6: 5-9)