In the traditional Christmas story, one of the important kids is Jesus. Mary and Joseph were his parents, and Jesus was born in Bethlehem which is a central part of the Christmas story.
In the traditional Christmas story, there is often the name Jesus as a central figure who was born as a baby. Also, there is the mention of the baby's mother Mary who was a young girl at that time.
There's also 'Nicholas'. Since Santa Claus is also known as St. Nicholas, having a character named Nicholas in a Christmas story can add a touch of authenticity. He could be a boy inspired by the story of St. Nicholas and tries to do good deeds like him.
There may also be children in the town of Bethlehem. But the story doesn't specifically name them. Their existence is more in the background, as the focus is mainly on Jesus, Mary, Joseph, the shepherds, and the wise men. But they would have been part of the community that was affected by the extraordinary event of Jesus' birth.
The most significant kid in the Christmas story is Jesus. His mother Mary and Joseph, his guardian, are important figures in the story too. There aren't really a whole bunch of other named kids in the traditional story, mainly it's centered around the birth of Jesus.