Is there any other internal system time that has to be set for the SD filesytem ?
Or issomethibg just not available for the Arduino File System ?
You can do it with an on-board RealTime Clock like the DS1307. In my projects, this is only used for backup to SD. Data aquired by local PC goes with the PC clock, and that sent over internet is timestamped at the other end.
You can use the clock to create a new file everyday, named with the date. It is then just a matter of printing the hour, minute, second to file along with the data.