Isaiah 48:9 - Ellicott's Commentary On The Whole Bible

For my name’s sake... — The thought is two-fold, in answer to the implied question why Jehovah had not punished so guilty a people: (1) after the manner of men, that had He destroyed His chosen people, the nations of the world would have thought Him changeable and capricious; (2) taking “name” as the symbol of character, that He might assert His own everlasting righteousness and love, as willing to save rather than destroy.