Grigoria’s name day is January 25, the feast of Gregory the Theologian.
Churches that follow the Old (Julian) Calendar keep the same feast on February 7 of the civil calendar. See everything commemorated on January 25.
The saint behind the name

Gregory the Theologian
January 25, Great Feast, Γρηγόριος ο Θεολόγος
St. Gregory the Theologian was born in Cappadocia in the fourth century and studied in Athens with his close friend St. Basil the Great. A man of deep prayer and unmatched eloquence, he was called to Constantinople when the city was dominated by Arianism, and through his celebrated theological orations restored the Orthodox faith in the Holy Trinity. He briefly served as Archbishop of Constantinople before withdrawing to a life of quiet and asceticism.
Also celebrating on January 25
These names share the feast, many of them other forms of the same name:
Grigorios, Grigoris, Gregory, Greg
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.