It is very simple: Jesus came in the Father's name. It is a shared name.
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, KJV)
Jesus' name is the only name whereby we must be saved.
10Be it known unto you all, and to all the people of
Israel, that by the name of Jesus Christ of Nazareth, whom ye
crucified, whom God raised from the dead, even by him doth this man
stand here before you whole. 11This is the stone which was
set at nought of you builders, which is become the head of the corner.
12Neither is there salvation in any other: for there is
none other name under heaven given among men, whereby we must be
saved. (Acts 4:10-12, KJV)
This name was already told us in prophecy before Jesus was born in Bethlehem.
For unto us a child is born, unto us a son is given: and the
government shall be upon his shoulder: and his name shall be called
Wonderful, Counsellor, The mighty God, The everlasting Father, The
Prince of Peace. (Isaiah 9:6, KJV)
The name given to Jesus was assigned to him before his birth.
And she shall bring forth a son, and thou shalt call his name JESUS:
for he shall save his people from their sins. (Matthew 1:21, KJV)
And, behold, thou shalt conceive in thy womb, and bring forth a son,
and shalt call his name JESUS. (Luke 1:31, KJV)
This "name" is the name of both Jesus (the Son) and the Father. This is the "name" into which we are to be baptized (see Matthew 28:19) and by which we are to be saved (see Acts 4:10-12).
Disclaimer: I am a non-trinitarian, but not a member of the Universalist or Unitarian church.