This psalm was clearly written after the destruction of Jerusalem by the Babylonian armies. It was a time of much suffering and calamity.
Still, the hope and faith in God are not extinguished. People are approaching God will repentance and sorrow. They know that their iniquity is big, and their pain is deep, but God above all moves for the honour of his name. They are his people, they want their deliverance to reflect God’s glory no their sin.
God put so much power in his name that at the name of Jesus every knee will bow down and every tongue will confess that he is God. ( Philippians 2:9-11)
There is power in the name of Jesus, in fact, there is no other name by which we must be saved. We can ask in his name, we can ask for his namesake anything.