The name Shem in the Bible
Noah was five-hundred years old when he fathered Shem and six-hundred when the flood hit, which means that Shem was a crisp century old when he and his family bobbed about in the Ark. Shem died in the year 502 AF (After the Flood), which is 35 years after Abraham died (in 467 AF).
At God's instructions Noah gathered a male and female couple of every animal, and seven individuals from every bird species and "clean" kind of animal. Since Noah also brought seven humans along (namely his wife and his three sons plus their wives), humans neatly fit the clean animal group or else the bird group.
After the flood receded and all creatures disembarked the Ark, Shem's brother Ham insulted his father and his son Canaan was cursed accordingly: Shem and Japheth were to live together in tents and Canaan was to be their servant.
Shem became the ancestor of Abraham and thus Jesus (Luke 3:36, where Shem is spelled in Greek as Σημ), and when the field of linguistics was invented, Shem also lent his name to the language group that Hebrew is part of: Semitic.
Shem, the man
Since Noah represents the whole of mankind (and his vineyard mankind's culture; see our articles on the words כרם, kerem, meaning vineyard, and יין, yayan, meaning wine), the brothers Shem, Ham and Japheth represent the most rudimentary inner structure of humanity, in both a sociological and psychological sense.
As more elaborately expounded in our article on the name Noah, Ham appears to denote mankind's most primitive, self-centered instincts and organizational structure of the chiefdom. Japheth's view goes beyond the personal and incorporates a theory of mind, develops oligarchy and democracy (two of Japheth's sons are Javan or Greece, and Madai or Persia) but remains convinced of the bi-polar, yin-yang nature of reality: "us," the good guys, versus "them," the bad guys.
The Shemite mentality, on the contrary, rises wholly above the self and views the world in absolute terms (that means: not relative to the self). To the Shemite, only natural law and verifiable knowledge of creation are important (John 4:22-24, Romans 1:20, 1 Corinthians 2:10, 1 Thessalonians 5:21), and that not for glory or reward, personal gain or even personal preservation (Isaiah 53:7, John 12:24, Romans 12:1-2) but in order to be a perfect steward of creation and thus the Creator (Psalm 24:1, Romans 8:19, Romans 13:8-10, 1 Timothy 6:17-19, 1 Peter 4:10).
To a Shemite, neither borders nor kinship nor human government nor perceived enemies nor religion nor symbols are of any importance (Genesis 12:13, Luke 9:23, 14:26-33, Revelation 21:22).
Etymology of the name Shem
The name Shem is equal to the word שם (shem), which itself means "name," whether it is meant as a regular name or as fame (to make a 'name' for oneself):
The name Shem means Name, Fame or Reputation. It even means Identity or Personality. For a meaning of the name Shem, NOBSE Study Bible Name List reads Name, Renown. Jones' Dictionary of Old Testament Proper Names has Name, but adds Celebrated, Distinguished.