While addressing the blessed Mary in 3:45, the name of Jesus is qualified with the phrase "son of Mary" to tell her he would be born without the agency of a father and therefore would be known with this name because to make the point clear that this child would have no father it would not have been enough to simply tell her she would bear a child as seen in Sara's case 11:71-3, hence Mary's astonishement as to what that statement implied in 3:47, ie the fact that she will be pregnant miraculously without a male touching her. In semitic tradition a person was identified by the father's name so nothing could have been more striking in the psyche of a woman of the time to be told that her son will not be identified by his affiliation to a male, but to a woman.
The phrase "son of Mary" also informs her that she would jointly share this sign with him forever as both of their names will be mentionned together 23:50,21:91"and made her and her son a sign for the worlds". Jesus is the only explicit case in the Quran where a human's birth did not result from sexual reproduction. The Quran doesnt even state that Adam was born in such a way. Jesus as well as his mother were chosen to be made jointly, "A" single sign of the power of the Maker and Creator over all things. So from a Quranic perspective, that miracle equally sets Mary and Jesus appart from humanity. This sign obviously consists in demonstrating how the process of resurrection isnt a difficult task, for how could it be hard for God to give life to anything when it was made possible for a female to give life without the necessary biological process?
The NT writers firstly wanted Jesus to be traced up to King David to fulfill the criteria for the Messiah's lineage, hence the introduction of an adoptive father, Joseph and the portrayal of Jesus as being known under the patronym "son of Joseph" in his community, and secondly tried "protecting" Mary's public image as the future mother of a superhuman being, saying she was engaged before her pregnancy and married when she delivered meaning the virgin birth was a secret yet this was, according to the NT writers that base themselves on the infamous mistranslation of Isa7:14 in the Greek Septuagint, of the most crucial fulfilements of OT prophecies the Israelites had to know from the very beginning to identify the awaited savior Isa7:14,Matt1:22"All this took place to fulfill what the Lord had said through the prophet: “The virgin will conceive and give birth to a son, and they will call him Immanuel". It is no surprise that in his purported letters, Ignatius the bishop of Antioch and supposed disciple of the apostles declares that Mary's virginity and child bearing were secrets only made known to the world through a "star". Jesus had to be known as special since the very beginning, according to specific criteria in order to be identified, yet not only was the virgin birth obscured to the people through the absurd introduction of a husband (whom the authors needed to establish a genealogy to king David) but the NT also repeatedly says how the young Jesus was completely unknown in any particular way prior to his ministry in adulthood, see Matt13 for example.
The absurdity doesnt end here, the same NT that tells us his people knew nothing special about him prior to his ministry also tells us of the all the wonderful signs and wonders surrounding his first moments as an infant, the celestial signs that prompted both friends and foes to look for him even from outside Palestine, people such as the Magi coming "from the east" to worship the newly born "king of the Jews", and king Herod who, fearing for his throne, began slaughtering all male infants born in Bethleem at that particular time which prompted Mary to flee with her son to Nazareth Matt2. Part of the NT establishes the fact that it was well known in and outside Palestine that the awaited savior had come, and countless people identified him with Jesus since his youngest days as seen from the time of Mary's miraculous conception which caused Elizabeth to refer to her as "mother of my Lord" as she saw her pregnant Lk1, the shepherds who rushed to Bethleem to see the newly born Messiah of whom the angels told them about and after seeing him Lk2:17"they spread the word concerning what had been told them about this child, and all who heard it were amazed at what the shepherds said to them" or Anna, the daughter of Penuel as well as Simeon who recognized in the newly born Jesus the awaited savior and told others about him Lk2, the astonishement of all learned people as they heard the child at the Temple displaying the wisdom and knowledge God granted him. This last incident is preceded by the unprobable scenario of Jesus' parents travelling from Jerusalem where they had attended Passover, back to their hometown of Nazareth and only noticing after a day's walk that the little Jesus had been left behind, prompting their return to Jerusalem, and only found him after 3 days search. Astoundingly, the NT writers also paint Mary and Joseph completely ignorant of what Jesus meant when he stated that he "must be concerned with the affairs of my Father" in response to Mary's scolding him because of his disappearance Lk2:42-50. Did Mary and Joseph suddenly forget all the miraculous signs and fame surrounding his infancy just 12 years after his birth, as if they had never heard of them and their obvious implications as regards his identity?
The Quran, far from copying the above NT absurdities, says the virgin birth was a miracle made known to all. It would be foolish to provide a miracle of virgin birth to demonstrate the special nature of a child, when the woman who is suppose to carry the child is married. The protection of the virgin birth reaches such an extent in the Quran that whenever Jesus is quoted as addressing the Israelites, he does not once call them "my people" or "my nation" as other Israelite prophets like Moses are quoted as saying in the Quran. Jesus always calls them "Bani Israel" because they, contrary to him, could trace their lineage up to Israel from their fathers, which wasnt his case.
Son of Mary is another testimony by those who believed in him that they recognize as true the miraculous circumstances of his birth. While the Quran does agree on certain points with the NT just as it does with the OT in other instances the Quran corrects the errors that have crept into these Books and further adds additional information. If Muhammad was copying from them, then one has to explain how the very subtle differences, which are loaded with meaning, let alone the major differences are there in the Quran.