Praise be to Allah.
Shaykh Muhammad ibn ‘Uthaymeen (may Allaah have mercy on him) answered this question by saying:
I do not know of any basis for this name in the Sunnah, i.e., that the mountain in ‘Arafah, by which the Prophet (peace and blessings of Allaah be upon him) stood, is called Jabal al-Rahmah (the Mount of Mercy). Since there is no basis for that in the Sunnah, it should not be called by that name. Perhaps those who call it thus realize that this is a great standing in which those who stand at ‘Arafah receive the forgiveness and mercy of Allaah, so they called it by this name. But it is better not to use this name, rather it should be called Jabal ‘Arafah (Mount ‘Arafah), or the mountain by which the Prophet (peace and blessings of Allaah be upon him) stood, etc.