This is the name conferred on Hebrew patriarch Jacob after the great prayer-struggle at Peniel (Genesis 32:28), because “as a prince he had power with God and prevailed” (See Jacob.)
Israel 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).
This name Israel is sometimes used emphatically for the true Israel (Psalm 73:1; Isaiah 45:17; 49:3; John 1:47; Romans 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 Samuel 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.