Charitine’s name day is October 5, the feast of Charitine.
Churches that follow the Old (Julian) Calendar keep the same feast on October 18 of the civil calendar. See everything commemorated on October 5.
The saint behind the name

Charitine
October 5, Holy Woman, Χαριτίνη
St. Charitina was a young Christian woman who suffered martyrdom during the persecutions at the beginning of the fourth century. An orphan raised by a pious guardian, she lived in prayer and purity, and when she was denounced as a Christian she confessed Christ boldly, enduring cruel tortures until she gave her soul to God.
Also celebrating on October 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.