Yes, it's true, his full name is Anastasios (in fact I provided this information on IMDB).
Sakis is a nickname that comes from his birth name like this:
Anastasios => Anastasakis => Sakis
This is quite common in Greece.
It's also true that his parents got divorced when he was about twelve. You haven't read about this because usually the biographies refer mostly to his carrer rather than his personal life.
Here is some more information about his childhood that he provided himself in an interview on Nikos Hatzinikolaou TV show right after he returned from Eurovision:
Indeed his parents were divorced when he was about 12 years old. He was
deeply hurt. Like most children in a similar situation he felt he was
responsible for the divorce and was trying to figure out what he did wrong.
When he grew up he realised that this is a classic symptom for children
after a divorce and got over it. Now he believes that people should get
divorced if they can't get along anymore and remain friends. His parents
are both alive and he seems to hold them both in high esteem. When he talks
about his mother his face lights up and sweetens instantly. He is in
regular communication with her although she still lives in Corfu island.
She didn't go to Istanbul with him but they talked on the phone and she was
very confident and encouraging.
The host of the show gave him a theatre program from a play that was on in
Corfu in 1976. In the last page there was the cast and we saw a picture of
Sakis at the age of 4! - he held a role in the play! (I've heard that both
his parents were actors) - This was probably his first appearance on stage
ever!
He started gymnastics at a very young age, 7-8 years old, and he walked to
the sports club on his own every day. Since his home was at the outskirts
of the town he had to walk several miles through the country where it was
often dark, so he used to sing all the way in order to entertain his fears.
He and his friends used to make their own musical "instruments" and pretend
they were a band playing their favourite songs. In Corfu everyone is
somehow involved with music, either playing some instrument or singing, he
remembers his grandmother having an excellent voice and when she was singing
they could hear her from several blocks away.
He was in the national pole vaulting team for teenagers and held a very good
record (I think it was 4.45 m).
At school he wasn't very good, he didn't like to study at home and he hated
Maths but he liked History and Religion. He is a very religious person
until today.
In the last year of High School he was asked to sing at the school party
where he performed songs from Elvis Presley and the Beatles. The owner of a
local dance-club saw him there and offered to hire him as a singer. His
parents had no objection to him becoming a professional singer, in fact they were
encouraging.
The following is from an interview to the greek magazine "Nitro", December 2003 issue:
He had his first sexual experience with a girl from Corfu when he was a
teenager. He considers that to be one of the three major turning points in
his life.
He has two scars (one on the left side of his neck, just below his ear and the other on his chest).
He has the one on the chest since he was very small. He and his friends
were pretending to be indians and cowboys. One of his friends threw a reed
cane at him and he managed to avoid it only partially.
The one on the neck is also from his childhood. During playing he was
running and slipped so he fell on a glass edge. At first he didn't notice
anything. He started walking and then realised that there was blood
running.
He often returned home wounded either from football or bicycles. His mother
had been used to that and didn't freak out any more...