The first time the name “Hebrew” is used in the Bible is in Genesis 14:13: “And there came one that had escaped, and told Abram the Hebrew; for he dwelt in the plain of Mamre the Amorite, brother of Eshcol, and brother of Aner: and these were confederate with Abram.”

According to Strong’s Exhaustive Concordance, “Hebrews” is word #5680 and originates from the name Eber (sometimes shown as Heber). “Hebrews” is patronymic, meaning “a component of a personal name based on the given name of one’s father, grandfather, or an earlier male ancestor” (Wikipedia). For example, the Amalekites were descendants of Amalek. The Hebrews were descendants of Eber.

The Brown-Driver-Brigg’s Lexicon Definition of the word is “one from beyond.” It can also mean a “region beyond” from Hebrew “avár” = to pass/to cross.

There are five men named Eber in the Bible. The first was the son of Shem, who was the son of Noah (Genesis 10:1, 11:11-26), and therefore likely the originating Eber.

The Hebrews were not called “Jews” until much later in biblical history. The term “Jew” first appears in 2 Kings 16:6, during the time of King Ahaz, long after the days of Abraham, Isaac and Jacob. By that point, the nation of Israel had split into two kingdoms—Israel in the north and Judah in the south—and the people of the southern kingdom became known as Judeans, or Yehudim, which is translated “Jews.” Originally, then, “Jew” referred specifically to someone from the tribe or territory of Judah. Over time, especially after the fall of the northern kingdom and later the Babylonian exile, the term expanded to describe all Israelites who remained faithful to the God of Israel.

So, while Abraham is rightly called a Hebrew, he would not have been called a Jew, because that designation arose many centuries after his lifetime.

Additional Resources about the split kingdoms:
Christian Questions Podcast
Episode #1271: “Am I Throwing Away My Life’s Greatest Privilege? (Part I)”
A tale of two opportunities, two kings and two failures
Preview Video
CQ Rewind Show Notes

Episode #1272: (Part II)
Recognizing and living up to the magnitude of our privileges in Christ

For children, parents and Bible class teachers:
Animated video: Why did the kingdom of Israel split?