For the Lord will not forsake his people, for his great name’s sake, because it has pleased the Lord to make you a people for himself. (1 Samuel 12:22)
The name of God often refers to his reputation, his fame, his renown. This is the way we use the word name when we say someone is making a name for himself. Or we sometimes say, that’s a “name” brand. We mean a brand with a big reputation. This is what I think Samuel means in 1 Samuel 12:22 when he says that God made Israel a people “for himself” and that he would not cast Israel off “for his great name’s sake.”
This way of thinking about God’s zeal for his name is confirmed in many other passages.
For example, in Jeremiah 13:11 God describes Israel as a waistcloth, or belt, God chose to highlight his glory, but which turned out to be temporarily unusable. “For as the waistcloth clings to the loins of a man, so I made the whole house of Israel and the whole house of Judah cling to me, says the Lord, that they might be for me a people, a name, a praise, and a glory, but they would not listen.” Why was Israel chosen and made the garment of God? That it might be a “name, a praise, and a glory.”
Written by John Piper
Full article at Desiring God