Kallistratos’s name day is September 27, the feast of Kallistratos.
Churches that follow the Old (Julian) Calendar keep the same feast on October 10 of the civil calendar. See everything commemorated on September 27.
The saint behind the name

Kallistratos
September 27, Martyr, Καλλίστρατος
St. Kallistratos was a Christian soldier who suffered during the persecutions at the turn of the fourth century. Discovered at prayer, he confessed Christ before his commander and was cast into the sea sewn in a sack; delivered unharmed, his courage and deliverance brought forty-nine of his fellow soldiers to believe, and together they received the crown of martyrdom by the sword.
Name days: Kallistratos, Callistratus
Also celebrating on September 27
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.