The root word for Nazareth and Nazirene are similar in both the hebrew and greek.
The hebrew NeTseR is used as most likely a play on words in the Hebrew, which is read right to left (Resh-Tsade-Nun : Strong's H5342) means a "figurative descendent". It's direct translation is "Sprout, Shoot, Branch" which used in Isaiah 11:1-refering to Meshiach (Messiah), but also 14:19, 60.21, Dan 11:7. NeTseR is also the root word for Nazereth so in Hebrew the word play would be obvious.
The Gospel of Mathew was written in Hebrew as attributed to the Apostolic Father Papias (Papias, 150-170 CE, quoted by Eusebius, Eccl. Hist. 3:39), and church Fathers, Ireneus (Ireneus, 170 CE, Against Heresies 3:1), Origin (Origen circa 210 CE, quoted by Eusebius, Eccl. Hist. 6:25). Knowing this we imagine there was a play on words, characteristic in Hebrew, in Matt. 2:23" Were Yeshua (Jesus) "...came to a town "NaTseReTh"(little branch) ... ","...Spoken by the Prophets...","...would be called a "NeTseR" (Branch). The greek "Nazoraios" (Strong"s G3480, translated Nazarene in english, would have been Resh-Zayin-Nun in Hebrew, see Amos 2:11,12, but Nazoraios may have been the closest translation in the greek in order to preserve the hebrew word play. It means a Nazirite; one who takes a Nazirite vow. However,we know Yeshuah (Jesus) never took a Nazarite vow since we know he drank wine which is forbidden to any Nazirite. In addition there is nowhere in the prophets that speak of Mashiach being a Nazarite, which is contrary to Mathews gospel.
On the other hand, another hebrew word for "Branch" is TsaMaCh, (Chet-Mem-Tsade in hebrew, Strong's H6780), see; Jer. 23:5, 33:15, Zech. 3:8, 6:12- all clear references to Meshiach, but also found in Isa 4:2, 61:11, , Ezek. 16:7, 17:9,10, Hos. 8:7, Psalm 65:11.
So the theme of "The Branch" referring to Meshiach, NeTseR in Matt. 2:23, TsaMaCh in Jer 23:5, 33:15, Zech 3:8, 6:12, all referring to Yeshua Mashiach, was spoken by the Prophets as well fulfilling Mathew's gospel.
Thus the entire statement of Matt 2:23 is fulfilled, but only if we assume a hebrew word play in an original hebrew Gospel of Matthew.