
Greeks have 'name days' besides birthdays as nearly each day of the year is dedicated to one of the Christian saints.
So, the day you are born means: you have a birthday and a name day related to that Saint of that particular day you are born on.
Although birthdays became more common, name days are still celebrated.
Yes, the Greek Orthodox religion plays a significant part in the lives of the Orthodox Greeks.
Click here for a list of name days. Or this more specific list.