Polyefktos’s name day is January 9, the feast of Polyeuktos.
Churches that follow the Old (Julian) Calendar keep the same feast on January 22 of the civil calendar. See everything commemorated on January 9.
The saint behind the name

Polyeuktos
January 9, Martyr, Πολύευκτος
St. Polyeuktos was a Roman soldier in Melitene of Armenia in the third century, and is honored as the first martyr of that city. Moved by the faith of his Christian friend Nearchos, he confessed Christ openly, refused to honor the idols, and was beheaded for the Lord he had only newly come to know.
Name days: Polyeuktos, Polyefktos
Also celebrating on January 9
These names share the feast, many of them other forms of the same name:
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.