Rahma: meaning of the name

وَمَآ أَرْسَلْنَٰكَ إِلَّا رَحْمَةً لِّلْعَٰلَمِينَ ۝١٠٧

And We have not sent you, [O Muḥammad], except as a mercy to the worlds.

Surah Al-Anbya, Verse 107

وَٱكْتُبْ لَنَا فِى هَٰذِهِ ٱلدُّنْيَا حَسَنَةً وَفِى ٱلْـَٔاخِرَةِ إِنَّا هُدْنَآ إِلَيْكَ قَالَ عَذَابِىٓ أُصِيبُ بِهِۦ مَنْ أَشَآءُ وَرَحْمَتِى وَسِعَتْ كُلَّ شَىْءٍ فَسَأَكْتُبُهَا لِلَّذِينَ يَتَّقُونَ وَيُؤْتُونَ ٱلزَّكَوٰةَ وَٱلَّذِينَ هُم بِـَٔايَٰتِنَا يُؤْمِنُونَ ۝١٥٦

And decree for us in this world [that which is] good and [also] in the Hereafter; indeed, we have turned back to You." [Allāh] said, "My punishment - I afflict with it whom I will, but My mercy encompasses all things." So I will decree it [especially] for those who fear Me and give zakāh and those who believe in Our verses-

Surah Al-A’raf, Verse 156

قُلْ يَٰعِبَادِىَ ٱلَّذِينَ أَسْرَفُوا۟ عَلَىٰٓ أَنفُسِهِمْ لَا تَقْنَطُوا۟ مِن رَّحْمَةِ ٱللَّهِ إِنَّ ٱللَّهَ يَغْفِرُ ٱلذُّنُوبَ جَمِيعًا إِنَّهُۥ هُوَ ٱلْغَفُورُ ٱلرَّحِيمُ ۝٥٣

Say, "O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allāh. Indeed, Allāh forgives all sins. Indeed, it is He who is the Forgiving, the Merciful."

Surah Az-Zumar, Verse 53

ثُمَّ تَوَلَّيْتُم مِّنۢ بَعْدِ ذَٰلِكَ فَلَوْلَا فَضْلُ ٱللَّهِ عَلَيْكُمْ وَرَحْمَتُهُۥ لَكُنتُم مِّنَ ٱلْخَٰسِرِينَ ۝٦٤

Then you turned away after that. And if not for the favor of Allāh upon you and His mercy, you would have been among the losers.

Surah Al-Baqarah, Verse 64