Knew her not - The doctrine of the virginity of Mary before the birth of Jesus is a doctrine of the Scriptures, and is very important to be believed. But the Bible does not affirm that she had no children afterward. Indeed, all the accounts in the New Testament lead us to suppose that she did have them. See the notes at Matthew 13:55-56. The language here evidently implies that she lived as the wife of Joseph after the birth of Jesus.
Her first-born son - Her oldest son, or the one who had the privilege of birthright by the law. This does not of necessity imply that she had other children, though it seems probable. It was the name given to the son which was born first, whether there were others or not.
His name Jesus - This was given by divine appointment, Matthew 1:21. It was conferred upon him on the eighth day, at the time of his circumcision, Luke 2:21.