What was the name of God's son before he was named "Jesus"?
The Only Begotten Son and Word of God, and also El Elohim and YHWH (all three persons of the Trinity are YHWH since all three are YHWH and El Elohim are names for God and the Father, Son and Holy Ghost are God, three coequal, coeternal and uncreated persons).
However we must be absolutely clear that at the time of our Lord’s Incarnation, when He was born and was named Jesus (Yehshua, the Galilean Aramaic form of Joshua, when means “YHWH Saves”) becoming Emanuel (God With Us), this did not constitute a change to his uncreated, immutable and impassabile Divine Nature. Rather in the Incarnation His Divinity was united with our created Humanity without change, confusion, separation or division, so that our fallen human nature could not only be restored but glorified, allowing us to inherit eternal life and become sons of God by adoption, by grace what Christ is by nature. As St. Athanasius, the author of the document that defined our 27 book New Testament canon, excluding all books we now regard as apocrypha, some of which came very close to being included like 1 Barnabas, as well as Patristic works which St. Athanasius agreed with but did not feel should be included in the New Testament, his belief and that of the majority of early church fathers being the New Testament should consist only of works by the Apostles and Evangelists of the first generation and not their immediate successors like St. Clement or St. Ignatius), and other portions of which came very close to being ommitted and actually were from many Bibles for many years - for instance, the Syriac Peshitta lacks 2 Peter, 2 John, 3 John, Jude and Revelation and these books only became accessible to the majority of Aramaic speaking Christians two centuries later when a translation by St. Philoxenus of Mabbug and St. Thomas of Harqel was included in Western editions of the Peshitta Bible, but those used by the Church of the East in the Nineveh Plains, Baghdad, Basra, Kerala and the Malabar Coast continued to only have the 22 books of the original translation.
We can positively exclude the possibility that Jesus Christ is St. Michael because aside from the fact that not one Biblical verse says explicitly that they are the same person, many verses expressly declare that Christ is one with the Father, fully God, the creator of all things, and is eternal (John ch. 1, John ch. 10, et cetera) and that in Him the fullness of the Godhead dwelled bodily. It is made clear He is not subordinate to the father.
Conversely the angels are repeatedly declared to be subordinate to God (and Christ is God) and as the messengers of God.
What is more, Christ is not a messenger but our Savior. And was fully incarnate and fully human, which is incompatible with being an archangel, for Scripture is clear that the Angels are spiritual beings.