ٱلْرَّحِيْمُ
The Merciful, The Beneficent
From the root ra-ha-mim (ر ح م), which has the following classical Arabic connotations: to have tenderness, gentleness, kindness to love to have mercy, to have pity to show favor and goodness to have all that is required for beneficence.
The name Ar-Raheem (in Arabic: ٱلْرَّحِيْمُ) comes from the same root as Ar-Rahman which refers to Allah’s attribute of being Merciful. Although similarly related the meanings are different. Ar-Rahman can be understood to refer to Allah as the origination/source of all mercy, whereas Ar-Raheem refers to its sustaining/infiniteness. Some view the name of Ar-Raheem as being merciful to His creation deserving of mercy (primarily the mercy reserved for the believers).
وَكَانَ بِٱلۡمُؤۡمِنِينَ رَحِيمٗا
And ever is He, to the believers, Merciful.
هُوَ ٱلَّذِي يُصَلِّي عَلَيۡكُمۡ وَمَلَـٰٓئِكَتُهُۥ لِيُخۡرِجَكُم مِّنَ
ٱلظُّلُمَٰتِ إِلَى ٱلنُّورِۚ وَكَانَ بِٱلۡمُؤۡمِنِينَ رَحِيمٗا
“It is He who confers blessing upon you, and His angels [ask Him to do so] that He may bring you out from darknesses into the light. And ever is He, to the believers, Merciful.”
Quran 33:43
Reference: MyIslam.Org