The Sura is named (Aal Imran – the Family of Imran) after they are mentioned in these verses.
The Holy verses here are about the divine choice of the prophets (peace be upon them), their progeny and Virgin Mary (peace be upon her).
There are four people who had been chosen:
– Adam (PBUH) the Father of Humanity who was chosen by making the angels bow to him and granting him reason and enjoinment.
– Noah (PBUH) who said: (“My Lord, do not leave upon the earth from among the disbelievers an inhabitant.) (of verse 26, Nooh). Then was the fatal flood which drowned all people except for the believers who followed Noah, and therefore, were the progenies out of them.
– The family of Abraham: All prophets are descendants of Abraham (PBUH) including Prophet Muhammad (saws), Ishmael, Isaac, Moses, Jesus Christ, John, Zechariah, David, Jacob, and Joseph.
– The family of Imran, who are part of the family of Abraham among whom a miracle happens: a prophet is born to them with no father. Such miracle never happened and will never happen to anyone. On the other hand, the Almighty never mentions names except in the story of Virgin Mary, the daughter of Imran (PBUH) because it’s such a great incident and a sign for Virgin Mary. Virgin Mary is chosen out of the family of Imran for the miraculous birth of Jesus Christ (PBUH).
Anyhow, there is a confusion whenever the family of Imran is mentioned because there are two Imrans, the father of Moses and the father of Virgin Mary. Nonetheless, the one mentioned here is Imran, the father of Virgin Mary, and the following verses indicate that.