Honestly I thought you were referring to a restaurant cause the point above it you mention Philippine Bread House, which is a restaurant, not a general area. But of course if I was talking to someone and they said Little India, then with context, I'd understand what they meant no problem.

Now, if somebody I was talking to said Curry Hill, then I would not understand what they meant lol. That sounds too weird to me, but whatever. I've never seen it in print either. Of course if you're saying that Indians that live there call it Curry Hill, then who am I to correct them. I guess I'm just not "in the know."