Son of the Living God is the name that Peter gave to Jesus (Yeshua‘) when he confessed that Jesus was the Messiah (Christ in Greek). When we compare the parallel accounts (Mark 8:29 and Luke 9:20) it is clear that this title is messianic. It is a simple declaration that Jesus is God’s son, with an emphasis on the fact that God is ALIVE.

Peter’s exclamation, “You are the Christ (Messiah), the Son of the Living God,” in the Greek text of Matthew 16:16.
Son of the Living God in Greek:
Ho hyios tou Theou tou zōntos
Strong’s Concordance numbers: 5207, 2316, 2198
Bible references: Matt. 16:16; John 6:69 (Amp, KJV)
And Simon Peter answered and said, Thou art the Christ, the Son of the living God. (Matthew 16:16 KJV)