Alaikumassalam wa rahmatullah,
Raham Dil could be formedf from Rahm (Persian for "mercy", from Arabic) and Dil ("heart" in Persian). Thus the full meaning could be "mercy of the heart", "softness of the heart", "compassion". Rahm is derived from a Quranic root, while Dil is Persian as said. You can say it is an Islamic name since it contains a word that's derived from a Quranic root, but whether you call it Islamic or not, it is a good name and Muslims can use it since it has a good meaning.
You can write and pronounce Rahm as Raham.