Albert Barnes Commentary Isaiah 48:11

"For mine own sake, for mine own sake, will I do it; for how should [my name] be profaned? and my glory will I not give to another." — Isaiah 48:11 (ASV)

For mine own sake - . The expression here is repeated to denote emphasis. He had thrown them into the furnace of affliction on his own account, that is, in order that his own name should not be profaned by their irreligion and idolatry, and that the glory which was due to him should not be given to idols.

For how should my name be polluted? - The sense is that it would be inconsistent with his perfections to see his name profaned without endeavoring to correct and prevent it; and for this reason, he brought these afflictions upon them. They had profaned his name by their irreligion and hypocrisy. In order to correct this evil and prevent it in the future, he had brought these national judgments on them and removed them to Babylon. The doctrine taught here is that when the conduct of God’s professed people is such as to dishonor God and to make his name a subject of reproach with the wicked, he will visit them with heavy judgments. He cannot indulge them in a course of life which will reflect dishonor on his own name.

And I will not give my glory unto another - (See the notes at Isaiah 42:8). The sense here is this. The Jews had, as a nation, been prone to ascribe to idols that which was due to God alone. To correct this and make an effectual reform, he had removed them to Babylon and doomed them to a long and painful captivity there. It may be added that the punishment was effectual, and that their long trial in Babylon served entirely to correct all their idolatrous propensities as a nation.