Israel had profaned the name of God. But, God was going to act in such a way that he would vindicate his name. Israel and the nations would know that God’s name is holy. They would know that he is the Lord.
In Ezekiel 43, we read about how Israel profaned the name the Lord. “And the house of Israel shall no more defile my name, neither they, nor their kings, by their whoring and by the dead bodies of their kings at their high places, by setting their threshold by my threshold and their doorposts by my doorposts, with only a wall between me and them. They have defiled my holy name by their abominations that they have committed, so I have consumed them in my anger. Now let them put away their whoring and the dead bodies of their kings far from me, and I will dwell in their midst forever.”
I think this is saying that Israel profaned God’s name by making what they were doing seem like that was what God was doing. They made it seem that their judgments, government, and kingdom were God’s. Yet, Israel was filled with all kinds of abominations, idolatry, and uncleanness. Ezekiel writes elsewhere that the priests and leaders of Israel did not distinguish between the clean and the unclean, the holy and the unholy.
But, God says there is a distinction between what is clean and unclean, holy and unholy. He calls us to be holy just as he is holy. We need to put away the things that are abominable, the things that God detests. We need to stop our idolatry, no longer putting anything above God. Then his name is vindicated and he dwell with us.