Kodrados’s name day is September 21, the feast of Quadratos the Apostle.
Churches that follow the Old (Julian) Calendar keep the same feast on October 4 of the civil calendar. See everything commemorated on September 21.
The saint behind the name

Quadratos the Apostle
September 21, Apostle, Κοδράτος
St. Quadratus was an apostle of the early Church who preached the Gospel in Athens and in Magnesia, bringing many to the faith of Christ. Tradition associates him with a written defense of the Christians presented to the emperor, one of the earliest apologies for the faith, and he ended his life as a confessor of Christ.
Name days: Kodrados
What to say on a name day
The Greek wish is Χρόνια Πολλά (Chronia Polla), “many years.” A call or a short message on the day is what people remember. See name day wishes you can send and what a name day is.