I am a bit confused by this. If Reena is borrowed into Arabic from some other language, it need not have a meaning in either Arabic or Persian. I am interpreting your question as the meaning of Arabic or Persian name Reena.
Reena is used in a large part of India as well, with no particular association with the Muslim religion which is sometimes a mark of Arabic or Persian origin. I asked this board about the Indian names Reena, Rita and Riya (only connection I know being they are all used in modern times by Hindus, and they all start with some version of the Ri sound). There are lots of sites which will give you some meaning, and I can think of a couple of Sanskrit derivations, but I came to this board to find the `true' meaning.
I got no response: maybe somebody will notice it this time :-(