Ioannikios’s name day is November 4, the feast of Ioannikios the Great.
Churches that follow the Old (Julian) Calendar keep the same feast on November 17 of the civil calendar. See everything commemorated on November 4.
The saint behind the name

Ioannikios the Great
November 4, Venerable, Ιωαννίκιος ο Μέγας
Venerable Ioannikios the Great was born in Bithynia in the eighth century and served for years as a soldier before leaving the world for the monastic life on Mount Olympus in Asia Minor. There he lived in great asceticism and prayer, receiving gifts of prophecy and wonderworking, and he stood with the venerators of the holy icons in the troubled years of iconoclasm.
Name days: Ioannikios
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.