There are 99 names for god in Islam, many of which enumerate the various qualities of his greatness, perfection, and his Majesty.
Egypt's Dar al-Iftaa explains the meanings of the name "Ar-Rahman".
In Arabic, the word "Ar-Rahman" is derived from the noun rahma, which means mercy. The name illustrates God’s infinite, unconditional, and overarching mercy.
Therefore, the divine appellation is he whose mercy encompasses all of his creation and prevails over everything in this world.
The name "Ar-Rahman" denotes a kind of mercy and grace that is exclusive to God Alone. It is he alone who endows his creation—the needy and the non-needy, the worthy and the unworthy—with his favors.
God says in the Quran, “My punishment—I afflict with it whom I will, but My mercy encompasses all things” (Quran 7: 156).
From the moment of creation through the journey of life and until death, everything one experiences, favorable or unfavorable, is a mercy from God though we may not understand the wisdom behind it.
He also said in a hadith Qudsi, “I am ar-Rahman. I created the raham (womb) and derived a name for it from My Name.”