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 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.