Question: Why is the Son of God called Jesus, that is, a Savior?
Answer: Because He saves us, and delivers us from our sins; and likewise because we ought not to seek, neither can find salvation in another.
And in Jesus: that is, I believe in Jesus Christ. The words, I believe, are to be repeated, because as we believe in God, the Father, so we also believe in the Son of God, according to what is written: “You believe in God, believe also in me.” “Believe me that I am in the Father, and the Father in me.” “I and my Father are one.” “This is the word of God that you believe on Him whom He has sent.” “He that believes on the Son has everlasting life.” “That all men should honor the Son as they honer the Father.” (John 14:1; John 14; John 11; John 10:30; John 6:29; John 3:36; John 5:23) This is a sure and well-grounded argument in support of the true Divinity of the Son; for faith under this form is worship due to God alone.
Touching the name, Jesus, which we are here to consider, we must not merely inquire into the etymology of it, what it imports, but we must consider more especially the office of the mediator, which is signified therein. The word Jesus signifies a savior, or the author of salvation, which God Himself ascribes to the mediator in the new Testament. The true etymology or import of the word was given by the angel when he said, “His name shall be called Jesus, for He shall save His people from their sins.” (Matthew 1:21) The Son of God is, therefore, called Jesus, the Savior in respect to His office, because He is our mediator, and saves and delivers us from the evil both of guilt and punishment; and that truly, because He is an only and perfect Savior. The salvation which He offers is righteousness and eternal life. This is inferred from the name itself, because He has not the name without the thing, but on account of the office.
Zacharias Ursinus, Commentary On The Heidelberg Catechism, p. 165