Names worked differently then
A modern last name usually belongs to a whole family and passes from one generation to the next. Biblical names were usually simpler. A person might be known by a personal name, then identified by whose child they were, where they came from, or what place they belonged to.
This mattered because many names were common. There are several men called Simon, James, Judas and Mary in the New Testament. So people used extra descriptions to make clear which person they meant. These were identifiers, not surnames in the way Smith or Patel is a surname today.
People were often named after a parent
One of the most common patterns was to name someone as the son or daughter of a parent. When Saul asks David who he belongs to after David defeats Goliath, David identifies himself through his father Jesse and his home in Bethlehem (1 Samuel 17:58). Family connections told others something about a person's household and place in Israel.
Simon Peter is called Simon Bar-jona by Jesus (Matthew 16:17). Bar is an Aramaic word meaning son, so this identifies Simon as the son of Jonah. The Bible's KJV wording preserves that Aramaic-style name rather than turning it into a modern surname.
And Saul said to him, Whose son art thou, thou young man? And David answered, I am the son of thy servant Jesse the Beth–lehemite.
Places could identify someone too
A person's town or region could function much like an added label. Philip tells Nathanael that he has found Jesus of Nazareth, and identifies Jesus with Joseph as well (John 1:45). Nazareth was the town people associated with Jesus' upbringing, so calling him Jesus of Nazareth distinguished him from others named Jesus.
This does not mean Nazareth was Jesus' family name. It was a geographical description. In the same way, Mary Magdalene is distinguished from other women named Mary, though the New Testament presents that as a name or identifying description rather than explaining it as a modern surname (Mark 16:9).
Philip findeth Nathanael, and saith unto him, We have found him, of whom Moses in the law, and the prophets, did write, Jesus of Nazareth, the son of Joseph.
Titles also became part of how people were known
Some names included a role or title. Jesus Christ does not mean that Christ was Jesus' last name. Christ comes from the Greek word for Anointed One, corresponding to the Hebrew idea of Messiah. It tells us who Jesus is, God's promised King and Saviour, rather than which family surname he carried (Matthew 1:1).
The Bible also uses descriptions such as Peter, meaning a rock or stone, for Simon, and apostle for those sent out by Jesus. These names and titles reveal something about a person's calling, character, family, or setting. Reading them carefully can make the people in Scripture feel more real, and it can help untangle who is who.