A prince is one who is born of a king.   

Who was Jesus born of?   His Holy Spirit Father

So, this title is identifying the Holy Spirit Father as Peace.   

The Holy Spirit is Peace.   

For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The Mighty God, The everlasting Father, The Prince of Peace. Isa 9:6 This conflicting description of a single being could not have come from a rational mind.     It came from the Holy Spirit who would fulfil these words in Christ Jesus.      Jesus was born of woman and His Holy Spirit and so He is the Mighty God, the Everlasting Father.     This means that the Father begat Himself!      The Holy Spirit is the Spirit of Jesus.     Jesus is the body of the Holy Spirit.     We are made in the image of our Creator.     We are Spirit Soul And Body and so also is our Creator.     His name is Jesus.