What was St. Joseph's full name?

At the time of Joseph, men were usually named as sons of their fathers, using 'ben' or 'bar'.

So, from Matthew 1:16, which states that St. Joseph's father was called Jacob, Joseph would have been called Joseph ben Jacob [Anglicised]. Or, from Luke 3:23, which states that Joseph's father was called Heli, he would have been called Joseph ben Heli.