The matter of Jesus' name is summed up well by one verse.
"I am come in my Father's name, and ye receive me not: if another shall come in his own name, him ye will receive." (John 5:43)
This is corroborated by Matthew 28:19 where Father, Son, and Holy Spirit are linked to a single name, both in English and in Greek (not three names). The disciples recognized this name, and baptized according to Jesus' instructions in that single name. See Acts 4:10-12; Acts 2:38; Acts 8:12,16; Acts 19:4-5; and Romans 6:3.
This is an erroneous interpretation.
Jesus is the name given to the Divine Son when He became flesh. So we can say that Jesus Christ has always existed, because we speak of Him as a Divine and Eternal Person, having His Deity in, from, and with the Father (
homoousios, consubstantial, of the same and very being of the Father as true and very God). But it is a name unique to the Son, for the Son alone took on flesh, was united to our nature, our essence, as a true and real human being; flesh of Mary's flesh, as her seed, the Son of David, the Seed of Abraham, the Son of Man.
The Father is not Jesus.
The Holy Spirit is not Jesus.
The Son is Jesus, Jesus is the Son. The Divine Son of the Father.
Jesus came in His Father's name, i.e. He came in the authority and power of His Father.
This is an idea that has deep biblical roots, that a name is not just a collection of sounds which identifies an individual. In Hebrew שֵׁם (shem) means "name", but also reputation, fame, renown; it speaks of character. In English we can see a comparable idea of name in expressions such as "in the name of the king"--it is an invocation of authority, to act on behalf of another because the other has authority, or reputation, etc.
When we see this "in the name of" language, that is what is meant: something done by the authority of another. We, therefore, pray in Jesus' name; we act and speak in His name. That is also the meaning of baptizing in or by the name of Jesus, it is His baptism, i.e. the baptism which He institutes by His own authority when He says "Go and make disciples of all nations, baptizing them". It is another way of saying Christian Baptism, as distinct from the various "baptisms" of Judaism, or the baptism of St. John the Baptist; Christian Baptism--the baptism which Christ our Lord instituted--is a distinct thing which is the mark and seal of the Christian by which a person is brought into the covenant of grace and made a new person (c.f. John 3:3-5, Romans 6:3-4, et al).
It does not mean that the Three Divine Persons of the Holy Trinity are all named "Jesus". There are not three Jesuses, there's only one Jesus, the Son of God, Eternally-begotten of the Father as Word and Son of the Father.
"In the name of the Father, Son, and the Holy Spirit" is not "in the name of Jesus"; it is the singular name of the Trinity (i.e. "Father, Son, and Holy Spirit") because we are speaking of the Trinity, and the singular authority of God the Holy Trinity. And because Christian Baptism is not a baptism into Christ only, but a baptism into the Holy Trinity whereby, by our union to Christ, we receive the free gift of sonship (Galatians 4:4-7), and therefore have been brought into, by grace, the life and love of the Holy Trinity: Christ's Father is now our Father, the Spirit of God, the Spirit of Christ, is the Spirit Himself who now dwells in us. This Trinitarian understanding of Holy Baptism is prefigured in the Lord's own baptism in the River Jordan, where the Son in the water is also met with the voice of the Father from heaven, and the Holy Spirit descending like a dove. All Three Divine Persons are present in Baptism.
It is not about formula, but about things much deeper and more significant: That by Christ's command His Church baptizes, and in baptizing disciples are made, by grace alone sinners estranged from God receive faith, and are united to Jesus Christ, and in Christ come to know the Father as Father, and have the Holy Spirit, whereby the sinner is forgiven, justified, receiving the full benefits of Christ's atoning work (which is once and for all), and is now in the Mystery of the Holy Trinity; and here we are being sanctified, called to carry our cross of discipleship, have the hope and promise of salvation, both now as gift through faith and in the end with the resurrection of the body.
Of course the Son comes in His Father's name, for the Son bears His Father's full authority as the Divine Son of the Father, full of grace and truth.
-CryptoLutheran