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a name applied to the Israelites in Scripture only by one who is a foreigner (Genesis 39:14, 17; 41:12, etc.), or by the Israelites when they speak of themselves to foreigners (40:15; Exodus 1:19), or when spoken of an contrasted with other peoples (Genesis 43:32; Exodus 1:3, 7, 15; Deuteronomy 15:12)
In the New Testament there is the same contrast between Hebrews and foreigners (Acts 6:1; Philippians 3:5).
The name is derived, according to some, from Eber (Genesis 10:24), the ancestor of Abraham. The Hebrews are “sons of Eber” (10:21).
The term “Hebrew” comes from Eber, but the descendants of Eber also include the “Habiru.” Discoveries at Ebla, in northern Syria, seems to indicate the founder and king of Ebla to be “Ebrim.” (Henry M. Morris, The Defender’s Bible)
Others trace the name of a Hebrew root-word signifying “to pass over,” and hence regard it as meaning “the man who passed over,” viz., the Euphrates; or to the Hebrew word meaning “the region” or “country beyond,” viz., the land of Chaldea. This latter view is preferred. It is the more probable origin of the designation given to Abraham coming among the Canaanites as a man from beyond the Euphrates (Genesis 14:13).
A third derivation of the word has been suggested, viz., that it is from the Hebrew word 'abhar, “to pass over,” whence 'ebher, in the sense of a “sojourner” or “passer through” as distinct from a “settler” in the land, and thus applies to the condition of Abraham (Hebrews 11:13).