He who wills goodness and mercy for all His creatures
Allah is Ar-Rahmaan (in arabic: ٱلْرَّحْمَـانُ). He is the One who blesses all his creation with prosperity and devoid from disparity. He is most merciful, kind, and loving towards all creation. His Rahma is all inclusive and embraces all.
From the root r-h-m 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.
From the 99 names we begin the journey to understanding just exactly who Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. As a way of developing His relationship with us, He tells us more about Him. The names most frequently used in the Qur'an are the names of Rahmah (i.e., His mercy). Every surah with the exception of Surah Taubah begins with recitation of this name in the Basmala (i.e., the bismillah). This is the first impression He would like all His believers to know is that He is the most gracious and the most merciful.
Qulid’ul laaha awid’ur Rahmaana ayyam maa tad’oo falahul asmaaa’ul Husnaa; wa laa tajhar bi Salaatika wa laa tukhaafit bihaa wabtaghi baina zaalika sabeela
There are 169 mentions of Ar-Rahman throughout the entire Qur'an. The one most famously referenced in works as an example is the above from Surah al-Isra, "Say, 'Call upon Allah or call upon the Most Merciful. Whichever [name] you call – to Him belong the best names.' And do not recite [too] loudly in your prayer or [too] quietly but seek between that an [intermediate] way." (17:110)
And so, before beginning any task, we often say “bismillah hir-Rahman nir-Rahim” which means “In the name of God, The Most Gracious, The Most Merciful.” If you start with this you are seeking help through these two names of His mercy. We understand that without Him nothing can be accomplished and so we seek His aid.
There are six names that refer to His mercy, kindness, and his generosity and they are Ar-Rahman, Ar-Raheem, Ar-Ra'uf, Al-Barr, Al-Karim, and Al-Wahhab. The name Ar-Rahman is reserved for Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ alone, it's a quality that can't be ascribed to anybody else. A person can be referred to as Ar-Raheem, meaning showing absolute mercy. But Ar-Rahman is understood to be all-encompassing mercy, so far reaching that it touches everything and everyone. A kind of mercy that knows no bounds. No one posses that kind of Mercy except Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. A person named Rahman must have the prefix Abdur, meaning servant of the merciful.
From the hadith, it comments on Allah's Rahmat (mercy), “Verily, Allah has one hundred portions of mercy. From one portion the creation has been given mercy by virtue of which there is mutual love between the people and ninety nine portions are reserved for the Day of Resurrection.” 
Abdullah ibn Amr reported: The Messenger of Allah, peace and blessings be upon him, said, “Those who are merciful will be shown mercy by the Most Merciful. Be merciful to those on the earth and the One in the heavens will have mercy upon you.” 
The belief in Allah's mercy is beneficial to a believer because it causes an individual to reflect on their ability to be merciful themselves. Narrated Jarir bin `Abdullah: Allah's Messenger (ﷺ) said, "Allah will not be merciful to those who are not merciful to mankind."  It also encourages a believer to do good, to act with virtue so that they can receive the mercy of their Lord, "As for those who believe and do good, the Most Compassionate will certainly bless them with genuine love" (Surah Maryam ayah 96)
'Umar b. Khattab reported that there were brought some prisoners to Allah's Messenger (peace be upon him) amongst whom there was also a woman, who was searching (for someone) and when she found a child amongst the prisoners, she took hold of it, pressed it against her chest and provided it suck. Thereupon Allah's Messenger (ﷺ) said: Do you think this woman would ever afford to throw her child in the Fire? We said: By Allah, so far as it lies in her power, she would never throw the child in Fire. ' Thereupon Allah's Messenger (ﷺ) said: Allah is more kind to His servants than this woman is to her child. 
 Source: Sahih Muslim 2753 Grade: Sahih (authentic) according to Muslim.
 Source: Sunan al-Tirmidhi 1924 Grade: Sahih (authentic) according to At-Tirmidhi
 Sahih al-Bukhari 7376
 Sahih al-Bukhari 5999 & Sahih Muslim 2754