The Prophet ﷺ said: “The most beloved of your names to Allah are ʿAbd Allah and ʿAbd al-Rahman” (Muslim 2132). The Companion ʿAbd al-Rahman ibn ʿAwf, one of the very first Muslims, is famous for his generosity; he was called ʿAbd ʿAmr before Islam and the Prophet ﷺ changed his name.
ʿAbd al-Rahman combines ʿabd, “servant”, with al-Rahman, “the Most Merciful”, a name of Allah from the root r-h-m of mercy and reserved to Him alone. The name affirms that one is the servant of the One whose mercy encompasses all things. It is written Abdul Rahman or Abdurrahman in English, Abderrahmane in the Maghreb and Abdurrahman in Turkey.
Say, "Call upon Allāh or call upon the Most Merciful [ar-Raḥmān]. 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.