In Genesis, no son is born to Noah after the Flood; his named sons were already part of the family aboard the Ark.
Genesis 7:13 identifies Noah, his wife, his sons, and their wives as those who entered the Ark. Genesis names the sons as Shem, Ham, and Japheth, and Genesis 9:18 again introduces them as Noah’s sons after the Flood. The text does not record a later-born son.
This question addresses a common confusion created by the chronology of Genesis 5:32 and Genesis 7. Noah is 500 when Shem, Ham, and Japheth are introduced, and he is 600 when the Flood arrives. Those numbers do not mean that another son was born between the Flood and Noah’s later episodes.
Genesis 9:28–29 then summarizes Noah’s life after the Flood and gives his total age at death. It does not add another child. Later traditions may expand genealogies, but the Genesis account names no post-Flood son of Noah.