Most Tamilians are given a name, like the western tradition, and usually use their father's name as a last name. A wife takes on her husband's name as her last name. However, it is becoming more popualr just to keep a single last name for all the family, instead of the father's name buisness.
Also, it was originally that a child was named after the grandparents (because it was the grandparent's priviledge to name them, and they would just give their own name). Nowadays, children get their own name, and use their grandparent's name as a "religious" name only.