Of the two disciples, one of them was named Andrew. He had a brother named Simon Peter. When Andrew encountered Jesus, he brought his bro Peter to Jesus because Andrew realized that Jesus is the Messiah (also known as the "Christ" or "Savior") (1:41-42).
Now Jesus saw Peter, and he gave him a new name -- Cephas. Translated as a stone.
The name is likely referring to a calling or title (especially since later on, Peter was called to be the foundation of the Church -- hence the word "stone"). Even with people newly introduced, Jesus still does stuff with them. Also pretty neat.