It's hardly surprising that you don't hear it.
Unless you live near a community of Christians who both know history, and still practice 2000 year old Christian vows or else you live near aramaic or syriac speaking peoples; you aren't likely to hear a Hebrew word in English. You're more likely to hear "tonsure' than 'nazir'. But that doesn't change the fact that the word itself, nazarite, nazirite, etc. means "vow" and is not strictly limited to the mosaic law and has a very deeply divided Christian history.
Consider:
John the baptist was an actual nazirite, in the mosaic law sense; consecrated within his mother's womb like Sampson.
And many people mistakenly thought John was the messiah (eg: the Christ), as the prophets had foretold -- BUT -- There was a dispute as to exactly how the ides of nazirite would fit into the prophecies which would led to deadly persecution between Christians and Jews. ( Matthew 11:18-19 )
(Note: In early Jewish scriptures, vowels with the exception of Aleph, were not written down until long after Jesus died. so, Nazirite, was originally written like Nazr when the prophecies about the messiah were recorded. Nazirite, Nazorite, Nazorean, are all words which *CAN* fit the same consonant pattern. I think it's likely a matter of the translator's choice as to what appears in any bible translated from the original languages before the time of Jesus. )
So -- the Nazirite status of the messiah was part of the (disputed) prophecies of the coming of the messiah (Matthew 2:23, Matthew 11:19). No prophet ever wrote down in scripture that Jesus would come from a town called "Nazareth"; rather they said he would come from "Bethlehem".
But even so, but the prople who stood to loose the most power when the messiah came were the Pharisees, and they didn't really care where he came from: the wished to kill both John the Baptist and Jesus as threats to their authority regardless of what the prophets said. The pharisees (and their fathers) were always getting the prophets killed.
Knowledge about the pharisaical disputes, and public acting out of those divisive beliefs along with caulumny / attempts to identify the Christian interpretations of those prophecies with illegal activities of thieves/brigands from Nazareth ( John 1:46 ) were very common when Paul wrote the letter to the Corinthians. We're at a disadvantage in interpreting these scriptures, because some of what has happened is no longer part of our present day experience as Christians and does not automatically come to mind when reading a scripture. We have to study and cross reference things in the bible to even get a glimmer of an idea of what was going on.
But it's plain to see in scripture that the secular authorities understood Christians to be Nazr's; Acts 24:5 because of accusations from the Jews -- and I mean, read Acts 20:17-40, and Acts 21:1-8 very carefully.
Notice that it begins with Paul who had shaved his own head on account of a vow, paying for four other Jewish Christians to have their heads shaved. And it is on account of this very activity that Paul gets arrested (his enemies using false accusations and mob violence) for breaking the laws of Moses. But notice that Paul, is said in Scripture chose to address the crowds in aramaic for his own defense (Eg: Aramaic is a Jewish variant/descendant of the Hebrew language; so that the ambiguity about "Nazr" was exploitable by Paul to confound his enemies. ) and it is in that language (not Greek) that Paul defends his own actions in the temple (eg: shaving of heads).
Now: Notice very carefully, that Paul suddenly refers to the vision he had on the road to Damascus as coming from Jesus (Which means "God saves in Hebrew/Aramaic) the "Nazr" (Nazorean/Nazirite/etc.) as part of his justification for what he had just done in the temple. eg: Paul specifically names "God saves the Nazr" as part of his defense for taking Nazirite vows and showing the falsity of the Jew's accusations against him.
And paul can do this truthfully because the law of Moses was written to speak/prepare for the messiah: ( Luke 24:44-45 ) -- eg: The Law of Moses isn't just about rules and regulations, it's about foretelling the prophet to come with power over the law (like Moses) to whom the people were commanded by Moses to "listen" (Deuteronomy 18:15) ( Even Today's Christians ought to listen to Jesus, riiiight ? )
The upshot of all this is that Christians were called "Nazareans" in the first century by civil authorities, ( Wikipedia
https://en.wikipedia.org/wiki/Nazarene_(sect) ) because a significant portion of Christian Converts were Jews, exactly like Paul, who still sometimes shaved their heads as a sign of "Christian" consecration but which did not break the law of Moses.
That practice, I think, became less common over time as Jesus' command to "convert all nations" led to the effect that Jews became the minority of Christians, as one nation among many who Jesus has brought into his fold. Besides which, the temple at Jerusalem was destroyed in 70A.D. So, there aren't Christians who could go there to finish the ritual even if they wanted to.
And it is precisely in this pre 70.A.D. context, while the temple still functioned -- that a Jewish Nazir (Paul), wrote the scriptures telling the Mixed Gentile and Jew community at Corinth about imitating
"Paul" (1Corinthians 11:1) And Paul says, in passing, that he himself imitates Christ, ( hmmm, but I wonder what that has to do with the shaving of heads ?? ) and don't forget Paul wrote this while still awaiting trial by the Romans, for the
same shaving of heads, no less... ) that got him arrested in Acts 20, this arrest -- just like Christ -- would eventually lead to Paul being put to death by the Romans, though he "did no wrong",and though paul's death was by circumcision at the neck -- not crucifixion.
Given this deep historical connection; It's difficult for me to see that 1:Corinthians 11 applies to modern Christian Women as a requirement of how they (or men) ought to wear head-coverings or not as a sign of "headship"; without any clear explanation of Paul's logic that is consistent with history.
Paul did command "Let the woman be shaven" -- Yet who obey's Paul's command in this modern Christian era or can explain why he would give such a command in context of his own imprisonment (shame) for having shaven his own head ? ( 1 Corinthians 11:5-6 ) Women could be Nazirites according to the Law of Moses, so his comments -- are very unclear.
There is something fundamental missing in the discussion.