Christ means 'anointed one' it's a title, not a last name.
If you can even count this as a last name, Jesus's last name would have been son of Joseph, or some sort of description of where he was from. He is Jesus the Christ, meaning he is the Messiah, like SpearmintMilk said.
I wanted to delete it... hey look. 4 people agreed! Even I said no way!