Akindynos’s name day is November 2, the feast of Akindynos and companions.
Churches that follow the Old (Julian) Calendar keep the same feast on November 15 of the civil calendar. See everything commemorated on November 2.
The saint behind the name

Akindynos and companions
November 2, Martyr, Ακίνδυνος
The holy martyrs Akindynos, Pegasios, Aphthonios, Elpidophoros, and Anempodistos were Christians of Persia who suffered in the fourth century, during a fierce persecution of the Church in that land. Refusing to deny Christ, they endured many torments and were put to death, and their steadfastness drew others to the faith.
Name days: Akindynos
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.