An important Christian tradition is that the brothers of Jesus, mentioned in the gospels, were born to Joseph by a previous marriage. Is there a name given to this tradition?
During the first century, the continuing virginity of Mary after the birth of Jesus does not appear to have been important. Matthew 1:25 concedes that Joseph and Mary began sexual relations after Jesus was born, or is at least ambiguous:
And knew her not till she had brought forth her firstborn son: and he called his name JESUS.
There was no full consensus on the doctrine of perpetual virginity within the early Church by the end of the second century ... However, wider support for the doctrine began to appear within the next century.
The church was moving towards a universal doctrine of Mary's perpetual virginity. The question was, where did the brothers and sisters, mentioned in Mark 6:3, Matthew 13:55, John 7:3, Acts 1:14 and 1 Corinthians 9:5, come from? Wikipedia again:
Origen (185-254) was emphatic on the issue of the brothers of Jesus, and stated that he believed them to have been the children of Joseph from a previous marriage. But careful analysis of this hypothesis brings up a number of problems, and it remains only one of several explanations put forward. Another popular hypothesis is that the term "brothers and sisters" actually meant cousins.
The Catholic catechism states (my emphasis):
499 The deepening of faith in the virginal motherhood led the Church to confess Mary's real and perpetual virginity even in the act of giving birth to the Son of God made man. In fact, Christ's birth "did not diminish his mother's virginal integrity but sanctified it." And so the liturgy of the Church celebrates Mary as Aeiparthenos, the "Ever-virgin".
500 Against this doctrine the objection is sometimes raised that the Bible mentions brothers and sisters of Jesus. The Church has always understood these passages as not referring to other children of the Virgin Mary. In fact James and Joseph, "brothers of Jesus", are the sons of another Mary, a disciple of Christ, whom St. Matthew significantly calls "the other Mary". They are close relations of Jesus, according to an Old Testament expression.
501 Jesus is Mary's only son ...
In summary, the thesis that the brothers and sisters of Jesus were the children of Joseph from a previous marriage is quite ancient, if not universally accepted among Christians, but does not appear to have a specific name.