Hi kaviri mainthan is surely another version of the name ponniyin selvan. of course the name was thought of ahead of the book.
ponniyin selvan itself is a take off of 'ponnu iyerin magan' as kalki was referred to in his village became ponniyin selvan.
i was talking to a agricultural scienist near ranipet. he tells me the river near thiruvallam the capital of vanthiyathevan is 'poinai'
the ancient name was "niva" talking about kalki and rivers ponni o kaveri was not his favourite river. his favourite was Palar. infact his last wish was to drink that river water. but then the water that was broguht by a friend came too late.