Diogenes’s name day is December 5, the feast of Diogenes the Martyr.
Churches that follow the Old (Julian) Calendar keep the same feast on December 18 of the civil calendar. See everything commemorated on December 5.
The saint behind the name
Diogenes the Martyr
December 5, Martyr, Διογένης
The holy martyr Diogenes confessed Christ before the pagans and, according to the Synaxarion, was perfected by stoning. His name is kept on this day in the Greek calendar.
Also celebrating on December 5
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.