Mat 2:23 and he went and lived in a town called Nazareth. So was fulfilled what was said through the prophets, that he would be called a Nazarene.
Nazarene isn't the name of someone who took the nazarite vow. (Jesus broke that vow several times if He had taken it)
Nazarene isn't the name of someone who lives in Nazareth. Of course it's bit related because the town was founded by David's family and the wanted to express the fact they are the bloodline of "the root of Jesse".
Isa 11:1 The royal line of David will be cut off, chopped down like a tree; but from the stump will grow a Shoot—yes, a new Branch* from the old root.
Isa 11:10 And in that day there shall be a root of Jesse, who shall stand as an ensign of the people; to it shall the Gentiles seek: and his place of rest shall be glorious
Branch is netzer in Hebrew. Netzer is a special type of branch that grows out of the roots of an olive tree that has been cut down. This netzer springs up a little distance from where the original tree stood.
The old roots are obviously the OT laws. The branch is still an olive tree (Law follower) but does things a little different.
In the NT we saw Jesus followed the same law as Judadism tree which was cut down. But His interpretation is at a little distance from the old tree.
Jesus is also called a "tzemach" which is the generic name for branch. That's no contradiction. Isa just gives a little more detail on the type of branch.
Jer 23:5 "The days are coming," declares the LORD, "when I will raise up for David a righteous Branch, a King who will reign wisely and do what is just and right in the land.
Zech 3:8 "'Listen, High Priest Joshua, you and your associates seated before you, who are men symbolic of things to come: I am going to bring my servant, the Branch.
Son of man-Branch.
Zech 6:12 Tell him this is what the LORD Almighty says: 'Here is the man whose name is the Branch, and he will branch out from his place and build the temple of the LORD.
Son of God-Branch.
Isa 4:2 In that day the Branch of the LORD will be beautiful and glorious, and the fruit of the land will be the pride and glory of the survivors in Israel.
Jer 33:15 In those days and at that time I will cause a righteous Branch to spring up for David, and he shall execute justice and righteousness in the land.