This verse is called the Basmalah, the first verse in the opening chapter (Al-Fatihah) and is a part of it. It is also written before each chapter of the Holy Qur’an though not considered as a part of these chapters.
Ar-Rahmah(الرّحمة) is Mercy, derived from Ar-Rahm (الرّحم) which literally means the womb. While Ar-Rahman (الرّحمن), the Most Gracious has a more intense meaning than the word Ar-Rahim (الرّحيم) the Most Merciful. His name Ar-Rahman (الرّحمن), the Most Gracious suggests that His mercy encompasses both towards the believer and non-believer, for this world and also the hereafter. This attribute of Allah U is exclusive to Him and none other. When used as an adjective to describe a human, we do not say ‘so and so is Rahman, rather, we describe them as the servant of Ar-Rahman (Abdur-Rahman). The word Ar-Rahim (الرّحيم) on the other hand, can be an adjective used for the believers as Allah U describes His Messenger r in the Holy Qur’an as:
﴾لَقَدْ جَاءَكُمْ رَسُولٌ مِّنْ أَنفُسِكُمْ عَزِيزٌ عَلَيْهِ مَا عَنِتُّمْ حَرِيصٌ عَلَيْكُم بِالْمُؤْمِنِينَ رَءُوفٌ رَّحِيمٌ﴿
“Truly, (O believers), a Messenger has come to you from among yourselves. It grieves him that you should suffer (in this life or in the life to come.) Ardently anxious is he over you and towards the believers he is most kindness and merciful.”. [Surah At-Tawbah: 128].