What was Mary and Joseph's last name?

Here's a fun question with an unusually complex answer. In biblical times, the last name of Jewish men was the name of their fathers. My dad's name is David, so if I were living in the time of Jesus my name would be Kainoa ben David. "Ben" means "son of" in Hebrew, and sometimes you see the Aramaic equivalent "bar" in the Bible as well ("Simon Bar-Jonah," Matthew 16:17).

What makes things complicated is trying to figure out who Joseph's father was. In Matthew 1:16 it says that Joseph's father was Jacob, yet in Luke 3:23 it says that Joseph's father was Heli. What's the deal?

There are several ways in which people have approached this, but I will offer only one. It was not uncommon for the Jewish writers of the Old Testament to leave out names in genealogies. In fact, what our English Bibles usually translate as "begat" or "son/father of" really means male descendent/ancestor of. Since my grandpa's name is Edward, if a biblical writer was writing my genealogy they would be correct if they wrote, "Edward was the father of Kainoa" or "Kainoa the son of Edward" because the importance is not on providing a detailed pedigree but on drawing a line between certain related individuals.

This is why Matthew's geneaology has fewer names then Luke, even if you only count the names from Abraham. Matthew appears to have selected the names that he did as a poetic device (Matthew 1:17) whereas Luke the physician might be more interested in Jesus' actual lineage.

To answer the question, Joseph was probably called either "Joseph ben Jacob" or "Joseph ben Heli."