Our family was just mentioning about Ramaadan, which is going on now-a-days.
Saint Mohammad got his divine revelation when he was in a cave meditating during the months of Ramaadaan, a practice much before Islam was introduced by him. This is yet another sign of Arabia practising Vedic beliefs. His nephew's wife name was Hindooja, which is a common Sindhi last surname.
Rama - as noun it means one who is "relished in the Self" with full delights. It is also an epithet for Lord Rama.
Daan - is noun for giving from the root "da", which means "to give".
A-daan - means "not daan", and it means opposite of "giving", which is "accepting".
So the word means "accepting of Rama" or "acceptance of God".
Persians for some reasons, made it "Ramaajaan".