Last names were commonly just where you were from, who was your father, or what was your profession.

Jesus Of Nazareth, or Jesus Denazareth, Jesus Nazarethton, Jesus Di’Nazareth, Jesus Von Nazareth, Jesus Van Der Nazareth.

Jesus Son Of Joseph, or Jesus O’Joseph, Jesus Josephson, Jesus McJoseph, Jesus Bin Joseph, Jesus Josephsen, Jesus Ibn Joseph.

Jesus the Carpenter, or Jesus Carpenter.

(Those are just examples from different languages of how last names were commonly created, not what they actually called Jesus.)

Christ was his status as a holy figure. Like the “saint” in Saint Peter. It means “the anointed one” or “messiah”.