Son of His love is a name of Jesus (Yeshua‘) that only appears in the Amplified Bible. Other versions have slightly different expressions in this verse, but they carry the same meaning: His beloved Son (NASB), the Son he loves (NIV), and His dear Son (KJV).
Son of His love in Greek:
Ho hyios tēs agapēs autou
Strong’s Concordance numbers: 5207, 26
Bible reference: Col 1:13 (Amp)
[The Father] has delivered and drawn us to Himself out of the control and the dominion of darkness and has transferred us into the kingdom of the Son of His love. (Colossians 1:13 Amp.)