Reason Jesus must have been a real person

[Fake Messiah]

if you are going to make up the virgin birth and correct lots of other issues (like Matthew did), why not fix Jesus' name as well? It really is supposed to be Immanuel.

Maybe because writer of "Matthew" was dumb as shit? Considering that in Isaiah 7:14 doesn't even say born from virgin but rather it was wrongly translated in Septuagint that "Matthew" was using. He was dumb enough not to know what it really says and also that the passage doesn't even speak about Jewish messiah.
Then again there are Christians even on this forum, who are quiet now, that claim that Immanuel is same as Jesus.

Another example is the story about Jesus being from Nazareth but being born in Bethlehem.

Actually Mark calls him "Jesus the Nazarene," while Matthew, John and Acts always call him "Jesus the Nazoraean."
It also seems "Mark" never intended to paint Nazareth as Jesus' hometown at all, like verses 2:1 and 9:33 he appears to have had Capernaum in mind as Jesus' home – a town which also had a handy messianic prophecy attached to it (Isaiah 8:21- 9:2), as Matthew tells us in his gospel (4:12-16).

myth of the Resurrection because there's no way an author would make women so important to the story (ie, Mary Magdalene finding the empty tomb, etc).

Actually "Mark" ends on very sexist note. You must remember that "original" Mark ends with 16:8 meaning that women saw the empty tomb but "they said nothing to anyone, for they were afraid."
So, women panicked and ran away in terror! Ain't that just like a dame? Mark's gospel was written, at the very least, 40 years after the time it describes. Blaming those silly hysterical women conveniently explains why no one had ever heard the story before now, not even Paul - or any other Christian writer, apparently, since no one ever mentions this appearance to the women. So "Mark" is using M. Night Shyamalanian's twist of telling you now that Jesus rose.

With that keep in mind that none of the gospels agree on their names. Or how many of them there were. Or what happened at the tomb. Far from being a lock on the validity of the story, the "account," or rather, the conflicting "accounts," of the women at the tomb shows that nothing was easier to make up.