Kathy’s name day is November 25, the feast of Catherine the Great Martyr.
Churches that follow the Old (Julian) Calendar keep the same feast on December 8 of the civil calendar. See everything commemorated on November 25.
The saint behind the name

Catherine the Great Martyr
November 25, Martyr, Αικατερίνη η Μεγαλομάρτυς
St. Catherine the Great Martyr was a noble and brilliantly educated maiden of Alexandria, martyred at the beginning of the fourth century. According to tradition, she confessed Christ before the emperor and bested in debate the philosophers gathered to refute her, leading many to the faith. After torture on the wheel, which was broken by grace, she was beheaded.
Name days: Aikaterini, Katerina, Katia, Katina, Kate, Cathy, Cat, Katherine, Kathryn, Catherine, Ekaterini, Kaiti, Katie, Kathy
Also celebrating on November 25
These names share the feast, many of them other forms of the same name:
Aikaterini, Katerina, Katia, Katina, Kate, Cathy, Cat, Katherine, Kathryn, Catherine, Ekaterini, Kaiti, Katie
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.