For this game, use 1-12 and then 1-(28, 30, 31) to generate a month and day:
http://random.org/integers/ That day will serve as your person's birthday. The namebank would be the saints on that day, or cognates (Agota can be Agatha, Henrik can be Henry, etc).
Alternatively, use existing or made-up birthdays and don't bother with generating :P
Here's the link to the calender of saint's days:
http://www.behindthename.com/namedays/
DH:
-DW:
-DS:
-DS:
-DD:
-DS:
-DD:
-DD:
-DD/DD: