Giving a name while doing circumcision? It was claimed that the recent tradition in Judaism to give a name to babies while doing circumcision, is documented already in the New Testament. Is it true?

I'm looking for the source / reference.
Giving a name while doing circumcision?

Catholics celebrated the Feast of the Circumcision on January 1st up until Vatican II.


  The Feast of the Circumcision of Christ is a Christian celebration of the circumcision of Jesus in accordance with Jewish tradition, eight days (according to the Semitic and southern European calculation of intervals of days) after his birth, the occasion on which the child was formally given his name.
  
  The circumcision of Jesus has traditionally been seen, as explained in the popular 14th-century work the Golden Legend, as the first time the blood of Christ was shed, and thus the beginning of the process of the redemption of man, and a demonstration that Christ was fully human, and of his obedience to Biblical law.
  
  The feast day appears on 1 January in the liturgical calendar of the Byzantine Catholic and Eastern Orthodox Churches.[4] In the General Roman Calendar, the 1 January feast, which from 1568 to 1960 was called "The Circumcision of the Lord and the Octave of the Nativity", is now named the Solemnity of Mary, Mother of God, and the Octave Day of the Nativity of the Lord. It is celebrated by some churches of the Anglican Communion and virtually all Lutheran churches. In these latter Western Christian denominations, the Feast of the Naming and Circumcision of Jesus Christ marks the eighth day (octave day) of Christmastide. - Feast of the Circumcision of Christ


The biblical basis for such a feast comes from the Gospel of Luke:


  21 And at the end of eight days, when he was circumcised, he was called Jesus, the name given by the angel before he was conceived in the womb. Luke 2:21


We can see that Scriptures indeed noted down that this was in fact an historical Jewish custom.

Other biblical references include the following:


  59 And on the eighth day they came to circumcise the child. And they would have called him Zechariah after his father. -Luke 1:59
  
  12 He who is eight days old among you shall be circumcised. Every male throughout your generations, whether born in your house or bought with your money from any foreigner who is not of your offspring. - Genesis 17:12
  
  22 Moses gave you circumcision (not that it is from Moses, but from the fathers), and you circumcise a man on the Sabbath. 23 If on the Sabbath a man receives circumcision, so that the law of Moses may not be broken, are you angry with me because on the Sabbath I made a man's whole body well? - John 7:22-23