Al-Faatiha 1:3

Allah said next,

الرَّحْمَـنِ الرَّحِيمِ

(Ar-Rahman (the Most Gracious), Ar-Rahim (the Most Merciful)) We explained these Names in the Basmalah. Al-Qurtubi said, "Allah has described Himself by `Ar-Rahman, Ar-Rahim' after saying `the Lord of the Alamin', so His statement here includes a warning, and then an encouragement. Similarly, Allah said,

نَبِّىءْ عِبَادِى أَنِّى أَنَا الْغَفُورُ الرَّحِيمُ - وَأَنَّ عَذَابِى هُوَ ٱلْعَذَابُ ٱلْأَلِيمُ

(Declare (O Muhammad ﷺ) unto My servants, that truly, I am the Oft-Forgiving, the Most Merciful. And that My torment is indeed the most painful torment.) (15:49-50) Allah said,

إِنَّ رَبَّكَ سَرِيعُ الْعِقَابِ وَإِنَّهُ لَغَفُورٌ رَّحِيمٌ

(Surely, your Lord is swift in retribution, and certainly He is Oft-Forgiving, Most Merciful.) (6:165)

Hence, Rabb contains a warning while Ar-Rahman Ar-Rahim encourages. Further, Muslim recorded in his Sahih that the Messenger of Allah ﷺ said,

«لَوْ يَعْلَمُ الْمُؤْمِنُ مَا عِنْدَ اللهِ مِنَ الْعُقُوبَةِ مَا طَمِعَ فِي جَنَّتِهِ أَحَدٌ، وَلَوْ يَعْلَمُ الْكَافِرُ مَا عِنْدَ اللهِ مِنَ الرَّحْمَةِ مَا قَنَطَ مِنْ رَحْمَتِهِ أَحَدٌ»

(If the believer knew what punishment Allah has, none would have hope in acquiring His Paradise, and if the disbeliever knew what mercy Allah has, none will lose hope of earning His earning.)

The second verse speaks of the Divine quality of mercy, employing two adjectives Rahman and Rahim of which are hyperbolic terms in Arabic, and respectively connote the superabundance and perfection of Divine mercy. The reference to this particular attribute in this situation is perhaps intended to be a reminder of the fact that it is not through any external compulsion or inner need or any kind of necessity whatsoever that Allah has assumed the responsibility of nurturing the whole of His creation, but in response to the demand of His own quality of mercy. If this whole universe did not exist, He would suffer no loss; if it does exist, it is no burden to Him.