The Son's Name, His Title, and His authority are merited by the work He did on the Cross.
Wherefore I also, after I heard of your faith in the Lord Jesus, and love unto all the saints, Cease not to give thanks for you, making mention of you in my prayers; That the God of our Lord Jesus Christ, the Father of glory, may give unto you the spirit of wisdom and revelation in the knowledge of him: The eyes of your understanding being enlightened; that ye may know what is the hope of his calling, and what the riches of the glory of his inheritance in the saints, And what is the exceeding greatness of his power to us-ward who believe, according to the working of his mighty power, Which he wrought in Christ, when he raised him from the dead, and set him at his own right hand in the heavenly places, Far above all principality, and power, and might, and dominion, and every name that is named, not only in this world, but also in that which is to come: And hath put all things under his feet, and gave him to be the head over all things to the church, Which is his body, the fulness of him that filleth all in all. - Ephesians 1:15-23
Let this mind be in you, which was also in Christ Jesus: Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men: And being found in fashion as a man, he humbled himself, and became obedient unto death, even the death of the cross. Wherefore God also hath highly exalted him, and given him a name which is above every name: That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth; And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father. - Philippians 2:5-11
In addition, Christ's Priesthood is tied to His Sonship. They are inseparable and eternal. His calling to Sonship is His calling to Priesthood.
That is why Christ did not honor himself by assuming he could become High Priest. No, he was chosen by God, who said to him, "You are my Son. Today I have become your Father." Hebrews 5:5 NLT
His work of Redemption is the essence of His identity and the reason He bears the marks of the nails in His hands, and the mark of the spear in His side.
Creation was all about the Cross. The Rest that Christ prepared for us by His death and resurrection, was ready since the Lamb slain from the foundation of the world, made the world.
For only we who believe can enter his rest. As for the others, God said, "In my anger I took an oath: 'They will never enter my place of rest,'" even though this rest has been ready since he made the world.
We know it is ready because of the place in the Scriptures where it mentions the seventh day: "On the seventh day God rested from all his work." Hebrews 4:3-4.
For these reasons, it would not be an adding to Scripture, but an harmonizing of the Scriptures, to say, all things were created by him, and for him: [and him crucified.] Colossians 1:16
If not for the plan of Redemption, what role would the Son fill?
