Hi.
I have rented cars in different parts of Greece and had a slight difference in requirements.
In the high season at a busy resort it may be better to reserve a car before you arrive, as demand is high.Normaly your pasport and full driving licence is required, an id card is normally not accepted.From the big companys you may be asked for a visa or mastercard number to take a deposit, in case of mishaps..then its refunded to your card when returned but watch out it may take a day or two before its back on your account, so if your releying on this money for holidays be carefull you dont go in minus.
I have had cars in SS and have not been asked for a deposit, but all are different.
hope this helps a bit