It's certainly not a common name, if even that. I'm Indian, and have never heard of someone called siri. "Shri" is often a part of longer names, though it's almost never used in isolation (I can't recall anyone whose first name was simply Shri), because it is also a word used in the same sense as "Mr." in English.
As for being a word in South Indian languages... it's possible that it's an archaic word, but it's certainly not used commonly, at least in Kannada (which is my first language).
Anyway, my point is that it shouldn't have been there in the wikipedia page as a "common Hindu name", but I should probably be discussing this on the wiki talk page rather than HN. ;-)