If Jesus had a last name it would probably have been "Nazareth", his hometown. Or maybe Josephson, if he were associated with his stepfather; or even Godson, according to his real father. But, they didn't have last names back then. That's why you hear "Simon Peter's son" or "Jesus of Nazareth" ie, for individual distinction between persons with the same first name.
Christ, as you know, is not Jesus's last name.
It's a title that means "the annointed one".
When you say "Jesus Christ", you are saying, "Jesus, the Annointed One".