Why was our Mediator called Jesus?
Our Mediator was called Jesus, because he saveth his people from their sins.1
Scripture proofs
The Westminster Assembly's proof texts (KJV). The bracketed numbers in the answer above mark the clause each set of references supports; expand a row to read the verses.
1 Matt. 1:21
And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins.
This doctrine across the Standards
Where the Confession and the Westminster Shorter Catechism treat the same matter, so the question can be studied alongside its parallel statements.
In the Westminster Confession
VIII.1 It pleased God, in his eternal purpose, to choose and ordain the Lord Jesus, his only-begotten Son, to …
It pleased God, in his eternal purpose, to choose and ordain the Lord Jesus, his only-begotten Son, to be the Mediator between God and man, the Prophet, Priest, and King; the Head and Saviour of his Church, the Heir of all things, and Judge of the world; unto whom he did, from all eternity, give a people to be his seed, and to be by him in time redeemed, called, justified, sanctified, and glorified.
→ VIII.1 · Of Christ the MediatorVIII.3 The Lord Jesus, in his human nature thus united to the divine, was sanctified and anointed with the …
The Lord Jesus, in his human nature thus united to the divine, was sanctified and anointed with the Holy Spirit above measure; having in him all the treasures of wisdom and knowledge, in whom it pleased the Father that all fulness should dwell; to the end that, being holy, harmless, undefiled, and full of grace and truth, he might be thoroughly furnished to execute the office of a mediator and surety. Which office he took not unto himself, but was thereunto called by his Father, who put all power and judgment into his hand, and gave him commandment to execute the same.
→ VIII.3 · Of Christ the MediatorIn the Westminster Shorter Catechism
Q.23 What offices doth Christ execute as our Redeemer?
Christ, as our Redeemer, executeth the offices of a prophet, of a priest, and of a king, both in his estate of humiliation and exaltation.
→ Open Q.23Q.24 How doth Christ execute the office of a prophet?
Christ executeth the office of a prophet, in revealing to us, by his Word and Spirit the will of God for our salvation.
→ Open Q.24Q.25 How doth Christ execute the office of a priest?
Christ executeth the office of a priest, in his once offering up of himself a sacrifice to satisfy divine justice, and reconcile us to God; and in making continual intercession for us.
→ Open Q.25Q.26 How doth Christ execute the office of a king?
Christ executeth the office of a king, in subduing us to himself, in ruling and defending us, and in restraining and conquering all his and our enemies.
→ Open Q.26