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