The name conferred on Jacob after the great prayer-struggle at Peniel (Gen. 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" (Josh. 3:17; 7:25; Judg. 8:27; Jer. 3:21), and the "house of Israel" (Ex. 16:31; 40:38).
This name Israel is sometimes used emphatically for the true Israel (Ps. 73:1: Isa. 45:17; 49:3; John 1:47; Rom. 9:6; 11:26).
After the death of Saul the ten tribes arrogated to themselves this name, as if they were the whole nation (2 Sam. 2:9, 10, 17, 28; 3:10, 17; 19:40-43), and the kings of the ten tribes were called "kings of Israel," while the kings of the two tribes were called "kings of Judah."
After the Exile the name Israel was assumed as designating the entire nation.
Easton's Bible Dictionary. M.G. Easton. 1897.