Rangachari Anand has written a good piece on how South Indian names work.
South Indian names confuse non-Indians, and even North Indians sometimes, because one's personal name conventionally comes at the end. In this example, Anand's father's name was Rangachari. But the naming system is flexible: Vijay Amritraj, the former tennis player, has reversed the order, putting his given name first and his father's name second -- as an adaptation to the western system. And sometimes, for example if one had a famous grandfather, the family might adopt that name as a permanent surname, dropping the father's name... Anand has done a good job of simplifying the matter.