I'm Indian/Pakistani and I'm having a hard time myself thinking of names that would "cross over" ... most names are so "different" that it's hard to think of one. Also I'm more paki than indian and so a lot of the names I'm thinking of are not that Indian-ish, yk?
Have you thought of taking one of the existing indian names and adapting it? A lot of people these days are making up their own names now over there. My dh's cousin named his dd "Alizah" then emailed everyone a few days later and said, "Oh, we just decided to change it to Alizeh."