Amfilohios’s name day is November 23, the feast of Amphilochios of Iconium.
Churches that follow the Old (Julian) Calendar keep the same feast on December 6 of the civil calendar. See everything commemorated on November 23.
The saint behind the name

Amphilochios of Iconium
November 23, Hierarch, Αμφιλόχιος
St. Amphilochios was Bishop of Iconium in the fourth century, a kinsman and friend of the great Cappadocian Fathers; St. Basil the Great addressed to him important letters on the canons and dedicated to him his treatise on the Holy Spirit. He labored against the Arian heresy and took part in the Second Ecumenical Council at Constantinople.
Name days: Amfilohios
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.