Isaiah 48:9

For my name’s sake will I defer mine anger, and for my praise will I refrain for thee, that I cut thee not off.

For His own name's sake God defers His anger, and for His praise He refrains from cutting off His wayward people Israel, specifically Judah, though they are undeserving and unworthy, doing so for His name and glory. His restraint preserves them despite their unworthiness as an act of mercy and concern for the honor of His own name. It is not because of their goodness, devotion, purity, or fear of Him, nor because the people or their leaders or the church are righteous or obedient.

In the verses that follow He explains that He has refined His people in affliction, yet acts for His own sake so that His name is not dishonored or polluted and His glory is not given to another. For this purpose He kept sending His servants the prophets, continuing to send them to call everyone to turn from his evil way and return to Him. Through Judah He would exalt His name among the heathen and make His merciful designs and the glory of the divine character plain to those wholly unacquainted with His attributes, so that even people unfamiliar with God would see its glory.

His patience in holding back preserves the opportunity for the wayward to repent and turn from their evil ways. Then they can become witnesses to His truth and monuments of His power and grace, so that the enemies of truth will not triumph.