According to Genesis, Shem is the first son of Noah named in the family list.
Genesis 5:32 introduces Noah’s three sons as Shem, Ham, and Japheth. They are also named in that order in several later passages. Shem is presented as an ancestor in the genealogy leading to Abraham, making his line especially important within the biblical narrative.
Genesis 9 describes an episode after the Flood involving Noah, Ham, and Noah’s other sons. Genesis 10, often called the Table of Nations, associates different peoples and territories with the descendants of Shem, Ham, and Japheth.
A common mix-up is to treat the order of names as a definitive statement about birth order. Genesis 10:21 contains wording that has been interpreted in different ways concerning Shem and Japheth, so the safest answer to the naming question is simply Shem, the first son listed in Genesis 5:32.