"Shem" means, roughly, "name", and can have the same implication of "reputation" as in English

[muriel_volestrangler]

The Hebrew noun שׁם (shêm) means "name." The most straightforward use of שׁם (shêm) is to mark the name of an individual as seen in Genesis 3:20: "The man named (שׁם, lit.: "called the name of" ) his wife Eve, because she was the mother of all living." The noun שׁם (shêm) can also be used figuratively to represent ones "reputation." For example, when God calls Abram in Genesis 12:2, God says: "I will make of you a great nation, and I will bless you, and make your name (שׁםך ) great"; and when constructing the Tower of Babel in Genesis 11:14, the people state: "Come, let us build ourselves a city, and a tower with its top in the heavens, and let us make a name (שׁם ) for ourselves." Biblical authors use the divine name as a means of embodying the character and evoking the reputation of God as can be seen in Jeremiah 33:2 "Thus says the LORD who made the earth, the LORD who formed it to establish it—the LORD is his name (שׁםו )." In fact, referring to God today as "HaShem," or "The Name," as in Leviticus 24:11, is a common way for many to refer to God without speaking the actual name of the deity.

There is a clear social concern in the Hebrew Bible surrounding the continuation of one's name through descendants. One of the more well-known examples of this concern is the practice of Levirate marriage. As described in Deuteronomy 25, Levirate marriage was a practice wherein a widow without a son would marry (or produce a child with) her deceased husband's brother in the hope of producing a male heir. If a son was born of this union, Deuteronomy 25:6 states that: "The firstborn whom she bears shall succeed to the name (שׁם ) of the deceased brother, so that his name (שׁםו ) may not be blotted out of Israel."

And in case you were wondering, yes, the "name" of Noah's son in Genesis 5:32 is the very original שׁם (Shêm), which also happens to be the origin of the word Semitic, as the biblical Shem is considered to be the forefather of the Semitic peoples (cf. Genesis 10:21 ff.).

https://bam.sites.uiowa.edu/RTL/shem

And "Jew"/the "Jud-" words come from "Judah", the ancient nation, with an apparent earlier derivation from "celebrated":

late 12c., Giw, Jeu, "a Jew (ancient or modern), one of the Jewish race or religion," from Anglo-French iuw, Old French giu (Modern French Juif), from Latin Iudaeum (nominative Iudaeus), from Greek Ioudaios, from Aramaic (Semitic) jehudhai (Hebrew y'hudi) "a Jew," from Y'hudah "Judah," literally "celebrated," name of Jacob's fourth son and of the tribe descended from him.

https://www.etymonline.com/word/Judaism