Albert Barnes 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 - For the promotion of his own honor and glory; that it might be seen that he is powerful and merciful. This is constantly given as the reason why God saves people; why he forgives sin; why he redeems the soul; why he delivers from danger and from death. Compare Ezekiel 36:22, 32; Isaiah 37:35; 43:25; 48:9; Jeremiah 14:7; Psalms 6:4; 23:3; 25:11; 31:16; 44:26. This is the highest reason which can be assigned for pardoning and saving sinners.

That he might make his mighty power to be known - (Exodus 9:16). Compare the notes at Romans 9:17.