All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Most scholars are of the view that it is disliked to be named with compound names the second part of which is Ad-Deen (the religion of Islam), like Noor (Light of) Ad-Deen; their evidence for this is that it includes a wrong claim. Shaykh Bakr Abu Zayd quoted their statements in his book “Tasmiyat-ul-Mawlood” (Naming the new-born child) and then he said: “The disliked names include the names added to the Name of Allaah, like Hasabu (Honour of) Allaah, Rahmatu (Mercy of) Allaah, Ni’matu (Grace of) Allaah, with the exception of ‘Abdullaah (Salve of Allaah) as it is amongst the most beloved names to Allaah.”
Similarly, naming someone with compound names the second part of which is Ar-Rahmaan (The Most Merciful) implies the same meaning for which it is disliked to be named with those names. Therefore, changing this name is desirable and not an obligation, so, if you can change it, then it is better, but if there is any hardship in doing so, then you may keep it as it is. For more benefit, please refer to Fatwa 92693.
Allaah Knows best.