Joseph is not the name of Jesus’ father. Mark 6:1ff does not mention the name of Jesus’ father, only that
of his mother Mary. The father’s name only appears in the later birth legends in Matt. 1f and Luke 1f.
Where does the name Joseph for Jesus’ father come from? Father figures are often called Joseph in the New Testament: in addition to Jesus’ father, we can mention Joseph of Arimathea (Matt 27:57) and Joseph of Cyprus, called Barnabas, an early Apostle to the Gentiles (Acts 4:36).
Joseph Barsabbas, the Apostles’ chosen candidate as the 12th Apostle to take Judas’ place, may also belong to this group (Acts 1:22).
Josephus, who describes Jesus as a Samaritan pseudo-Messiah, mocks the name of Jesus’ father when he claims: if things are going well for the Jews, the Samaritans call themselves sons of Joseph; if not, they say they are descended from foreigners: Ant. 9.14.3.