It is not very clear what you are searching. Is it your family's history? Is it a specific person?
Anyway, Your REAL name is Fytris (Φυτρης). Φυτρακης (Fitrakis) is the little Fitris. The earliest record is from Malia, a village 32km East of Heraklion.
A Priest, Pappa-Konstantinos Fitris was killed 1821 (Cretan revolution) by the Turks. His belongings, a house, a piece of agricultural land, a small vineyard and 15 carob trees were left to his wife Marigo and their son Manolis.
Probably, Manolis Fitris, being an orphan, became the first Fitrakis.
I am quite sure the name does not exist in Malia today.