1:9 Then said God, Call his name Loammi: for ye are not my people, and I will not be your God.
1:10 Yet the number of the children of Israel shall be as the sand of the sea, which cannot be measured nor numbered; and it shall come to pass, that in the place where it was said unto them, Ye are not my people, there it shall be said unto them, Ye are the sons of the living God.
"My people" is an expression used in the O.T. exclusively of Israel the nation. It is never used of the patriarchs, Abraham, Isaac, and Jacob. Matthew 2:6 .
"Israel" in Hosea means the ten tribes forming the northern kingdom as distinguished from "Judah" (the tribes of Judah and Benjamin) forming the southern kingdom which adhered to the Davidic family. (See) 1 Kings 12:1-21 . The promise of verse 10 awaits fulfilment. See "Israel" ; Genesis 12:2 Genesis 12:3 ; Romans 11:26 .