John Gill Commentary Psalms 106:8

"Nevertheless he saved them for his name`s sake, That he might make his mighty power to be known." — Psalms 106:8 (ASV)

Nevertheless, he saved them for his name's sake
Not for any worth or worthiness in them; not for their righteousness sake, for they were a rebellious and disobedient people; but for his name's sake, because his name was called upon them, and he was called the God of the Hebrews, as Aben Ezra observes; and the God of Abraham, Isaac, and Jacob, their ancestors; to whom he had promised the land of Canaan, and was their covenant God; and because of his covenant, and of his divine perfections, and the glory of them, which were engaged to make it good; therefore he saved them, see (Ezekiel 20:9Ezekiel 20:14) .

And so the spiritual Israel of God are saved, not for any superior excellencies in them, for they are in no wise better than others; nor for their righteousness sake; but to display the wisdom and faithfulness of God, his grace and mercy, his justice and holiness, power, goodness, and truth. And so here it follows;

that he might make his mighty power to be known ;
not only among the Israelites, but among the nations of the world; who, had he not saved them, might have thought, and said, that it was for want of power, and that he could not do it; see (Deuteronomy 9:28) .