James son of Alpheus...that's about the closest I could get to a full name. Jesus's full name in Hebrew was Yehoshuah. I'm not sure what it was in aramaic. I hope that is a start for you.
Do you mean the "son of ___" aspect? Because I don't think they had last names back then.
If you recall, Jesus was called and known as the "son of a carpenter." That's how they were identified. Even teo of His disciples- James and John were sons of Alpheus (I don't know if that's how it's spelled).
Let me know what you're looking for. I'll try to help you out.
Still thinking about Biblical last names. When I come across anything I will post it.
"Question: "Did the people in the Bible have last names?"
Answer: People in Bible times did not really have last names like we do today. People frequently went by something similar to “Simon, son of Jonah” (Matthew 16:17). The phrase “son of Jonah” identified Simon as a different Simon than all the other Simons. This functioned very closely to a last name. Others used their occupation as a functional last name “Simon the tanner” (Acts 10:6). Jesus was sometimes called “Jesus of Nazareth” identifying where He was from (Matthew 26:71; John 18:5). The name “Jesus Christ” refers to “Jesus, who is the Christ / Messiah.”
Recommended Resource: Bible Answers for Almost all Your Questions by Elmer Towns."