AR RAHMAN: THE MERCIFUL or The Beneficent
He who wills goodness and mercy for all His creatures
who repeats this Name 100 times after each fardhu (obligatory) prayer will have good memory, a keen awareness, and be free of a heavy heart.
AR RAHIM: THE COMPASSIONATE or The Merciful
He who acts with extreme kindness
who repeats this Name 100 times after each Fajr (early morning) prayer will find everyone to be friendly towards him and show easiness to him