Hebrew

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a member of an ancient people living in what is now Israel and Palestine and, according to biblical tradition, descended from the patriarch Jacob, grandson of Abraham. After the Exodus ( c. 1300 BC) they established the kingdoms of Israel and Judah, and their scriptures and traditions form the basis of the Jewish religion.

First mention of a Hebrew is found 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.

All the other references in the Old Testament (14) refer to either men or women as Hebrews:  

GENESIS 39:14, 39:17, 41:12
EXODUS 1:15-16,19 2:7,11, 21:2
DEUTERONOMY 15:12
JEREMIAH 34:9,14    
JONAH 1:9

And in the New Testament, Hebrew refers to the language spoken or written:

LUKE 23:38
JOHN 5:2, 19:13,17,20
ACTS 21:40, 22:2, 26:14
REVELATION 9:11, 16:16

Only when Paul is testifying about his heritage is Hebrew referred to a people:
PHILIPPIANS 3:5 Circumcised the eighth day, of the stock of Israel, of the tribe of Benjamin, an Hebrew of the Hebrews; as touching the law, a Pharisee;

TO CONCLUDE, Abram was from a tribe know as Hebrews. Abram became Abraham, the father of Isaac, the father of Jacob who became Israel.