Kornilios’s name day is September 13, the feast of Kornelios the Centurion.
Churches that follow the Old (Julian) Calendar keep the same feast on September 26 of the civil calendar. See everything commemorated on September 13.
The saint behind the name

Kornelios the Centurion
September 13, Saint, Κορνήλιος
St. Cornelius was a Roman centurion stationed at Caesarea, a devout man who feared God, gave alms generously, and prayed continually. As the Acts of the Apostles relates, an angel directed him to send for the Apostle Peter, and he and his household became the first Gentiles to be baptized into Christ.
Name days: Kornilios
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.