ar Rahman and ar Raheem
Bismillah.
Ar-Rahman: The Entirely Merciful, Ar-Raheem: The Especially Merciful
Both of the names Rahman and Raheem come from the root Ra-ha-meem (ر ح م), these names are similar so they require a parallel explanation. What is Rahmah? Rahmah is mercy. In the dictionary it means: compassion, kindness and gentleness. Also when a person is kind, compassionate and tenderhearted towards the other. So Ar-Rahman and Ar-Raheem: The One who has a lot of Rahmah, The One who shows a lot of rahmah, He expresses a lot of Rahmah.