Mr_M, some attribute the introduction of surnames to the Normans in the 11th Century AD/CE. Prior to that, naming conventions generally used the first name.  Individuals were typically identified by:

• <First Name> son/daughter of <Father's First Name>; or,
• <First Name> of <Place Name>

With this in mind, Jesus would have been known as Jesus son of Joseph.

 

Joseph would have been known as Joseph son of Jacob (according to Matthew).

 

Mary would have been called Mary daughter of Eli.  Luke calls Mary's father Heli, which is the Greek for the Hebrew Eli.  Another apocryphal gospel describes Mary's parents as Joachim and Anna.  Joachim is considered a variant of Eliachim or Elohim or Eli or Heli.