As Christ wished to fulfill the law and to show His descent according to the flesh from Abraham. He, though not bound by the law, was circumcised on the eighth day (Luke 2:21), and received the sublime name expressive of His office, Jesus, i.e. Saviour.
A significant amount of art and imagery depicts the sacred event being performed by a priest in the temple, or in synagogue. However there are some paintings, and some Catholic authors who in fact have the event being performed by St. Joseph. It is my opinion, along with some of the Doctors of our Faith, that the later is the accurate. As my dribblings on St. Joseph are inadequate, I instead quote from Edward Healy Thompson's book titled: "The Life and Glories of St. Joseph". Emphasis mine:
But who was the minister of the rite? The Evangelist is silent on this point. Imagination has accordingly allowed itself full scope, and painters have been pleased to introduce into their representations a priest in his sacerdotal vestments; but we have no authority for supposing that any priest came to the stable of Bethlehem to circumcise Jesus. The opinion of those doctors who believe that the minister of the circumcision of Jesus was Joseph appears the most probable. St. Ephrem the Syrian, a most ancient writer and contemporary of St. Basil, one who was well acquainted with the traditions of his native land, and highly esteemed both for his science and his piety, says expressly that it was Joseph who circumcised Jesus. Writing in confutation of those heretics who ascribed to our Lord a phantastic body, he says: "If Jesus Christ had not true flesh, whom did Joseph circumcise?" Thus he refers to it as to an unquestioned fact. St. Bernard, Suarez, and many others also believe that Joseph circumcised Jesus, because he who circumcised an infant was the same also who imposed the name; and it was Joseph who gave Jesus His name. This opinion, then, has been generally adopted. The precept of circumcision was addressed to the heads of families; it was the office of the father, unless a priest took his place.
There is nothing written there that is overly remarkable. It contains evidence and facts or support for something much deeper. (Please pray to the Blessed Virgin before reading this next quote.)
Joseph, then, as Isolano says, circumcised Jesus as his son. On him we may believe devolved this solemn and painful duty. Jesus was circumcised by Joseph on Mary's knees, no other eyes beholding the first drops of the Precious Blood flow except those of the holy angels, and no other ears save theirs hearing the wail of the Divine Infant. In this act Joseph accomplished three sacrifices in one: the sacrifice of Jesus, who began the great work of our redemption by suffering in His innocent members; the sacrifice of Mary, who with indescribable sorrow, but with perfect resignation, offered her Son to the Eternal Father, and held, as it were, the victim bound; and the sacrifice of himself, who had to nerve his hand to perform an act so painful and repugnant to his tender heart. It was an act of heroic obedience and fortitude on his part, greater, St. Bernard says, than was that of Abraham in sacrificing his son Isaac; for Joseph loved Jesus incomparably more than Abraham did his son Isaac, and well knew the difference between the son of any mortal man and the Son of the Eternal God. Thus the knife which cut the flesh of Jesus wounded the heart and pierced the soul of Joseph. Here there was no angel to stay his hand. The act must be accomplished, and in performing it Joseph was, indeed, more than a martyr.
Then, too, was that name pronounced over the Divine Infant at which "every knee," as the Apostle tells us, should bow of those who are in heaven, on earth, and under the earth; and it was by the lips of Joseph that it was pronounced. St. Luke only says that His name was called Jesus, without specifying by whom; but from St. Matthew it would appear that it was Joseph; for the angel had said to him: "Thou shalt call His name Jesus". It was, indeed, no little glory to Joseph to receive an embassage from Heaven commissioning him to confer this name. Jesus is the Son of the Eternal Father; to the Eternal Father, therefore, it belonged to impose the name; and yet He commissioned St. Joseph to exercise that right in His place. Joseph, says Isidoro Isolano, is the Enos of the New Testament, who first began to invoke the Name of the Lord. That profound theologian, Salmeron, who was present at the Council of Trent, did not scruple to say that in this sole act of giving to Jesus His name was declared the whole paternal office of Joseph, as by the sole act of feeding the sheep of Christ was signified the full power and jurisdiction of Peter over the Church. Whence Isidoro Isolano draws the conclusion that Joseph in God's sight is superior to all the other saints, because no other was exalted to so high a dignity.
St. Joseph, circumcisor of God, Pray for us.
St. Joseph, name conferrer of God, Pray for us.