Regarding Jesus as the Branch:
Isaiah 11:
Righteous Reign of the Branch
1 Then a shoot will spring from the stem of Jesse,
And a Branch from his roots will bear fruit.
2 The Spirit of the LORD will rest on Him,
The spirit of wisdom and understanding,
The spirit of counsel and strength,
The spirit of knowledge and the fear of the LORD.
Word study:
Branch in Hebrew
netser: Branch, shoot, sprout
Original Word: נֵצֶר
Part of Speech: Noun Masculine
Transliteration: netser
Pronunciation: NAY-tser
Phonetic Spelling: (nay'-tser)
Definition: Branch, shoot, sprout
Meaning: a shoot
Word Origin: Derived from the root נָצַר (natsar), meaning "to watch" or "to guard."
New Testament:
Nazirite and Nazareth
nazir: Nazirite, one who is consecrated or set apart
Original Word: נָזִיר
Part of Speech: Noun Masculine
Transliteration: nazir
Pronunciation: naw-zeer'
Phonetic Spelling: (naw-zeer')
Definition: Nazirite, one who is consecrated or set apart
Meaning: separate, consecrated, an unpruned vine
Word Origin: Derived from the root נָזַר (nazar), meaning "to separate" or "to consecrate."
Corresponding Greek / Hebrew Entries: -
Strong's G3480: Ναζιραῖος (Naziraios) - Refers to a Nazirite or someone from Nazareth, depending on context.