Hebrew

a name applied to the Israelites in Scripture only by one who is
a foreigner (Gen. 39:14, 17; 41:12, etc.), or by the Israelites
when they speak of themselves to foreigners (40:15; Ex. 1:19),
or when spoken of an contrasted with other peoples (Gen. 43:32;
Ex. 1:3, 7, 15; Deut. 15:12). In the New Testament there is the
same contrast between Hebrews and foreigners (Acts 6:1; Phil.
3:5).

Derivation. (1.) The name is derived, according to some, from
Eber (Gen. 10:24), the ancestor of Abraham. The Hebrews are
"sons of Eber" (10:21).

(2.) 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 (Gen. 14:13).

(3.) 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 (Heb. 11:13).