The meaning of Israel in the Bible
(From Easton's Bible Dictionary)

the name conferred on Jacob after the great prayer-struggle at Peniel (Genesis 32:28), because "as a prince he had power with God and prevailed." (See JACOB .) This is the common name given to Jacob's descendants. The whole people of the twelve tribes are called "Israelites," the "children of Israel" (Joshua 3:17; 7:25; Judges 8:27; Jeremiah 3:21), and the "house of Israel" (Exodus 16:31; 40:38).

See more on the meaning of Israel in the Bible:
Israel {International Standard Bible Encyclopedia}
Israel {Hitchcock's Bible Name}

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