Below are the contact details for Cyprus' regiteries. They tend to record most, if not nearly all births from around the early 1900s onwards. They also have some deaths recorded, particularly in recent years and some marriages.
From experience, a birth record in Cyprus tends to contain the following;
A birth record in earlier times 1900-even up to the mid to late 1940s contained the following. Name of child, Both parents names, including mother's maiden name, DOB, place of birth, and sometimes even a father's occupation. On birth records in this period children did not tend to have a surname recorded on their birth. According to the patrynomics surname tradition; if a child named Georgios was born to Christodoulos Hadjigeorgiou, the child's full name was thus - Georgios Christodoulou Hadjigeorgiou. In most instances the child would only take on his father's first name as his surname. So in this case Georgios would be known as Georgios Christodoulou. Since their were no established hereditary surnames, many land records of the time state a person's three names according to the registry; "Child's name Father's first name Father's surname."
It may help alot of you, trying to find out actual names of ancestors from registry records, birth dates and even additional information on parents and their births and deaths. My advice is it is probably best to ring them (I have found the Paphos registry to be very helpful in providing birth and death details for free, also many staff speak English)
Here are the relevant BDM contact details for each district of Cyprus;
Nicosia District Office
Larnaca District Office
Limissol District Office
Tel: +357 25806400
Fax: +357 25305288
Paphos District Office
Famagusta District Office
Kyrenia District Office
Tel: 357-22867620, 867784
Hope it helps!