Mimi’s name day is October 26, the feast of Demetrios the Great Martyr.
Churches that follow the Old (Julian) Calendar keep the same feast on November 8 of the civil calendar. See everything commemorated on October 26.
The saint behind the name

Demetrios the Great Martyr
October 26, Martyr, Δημήτριος ο Μεγαλομάρτυς
St. Demetrios the Great Martyr and Myrrh-Streamer was a young nobleman and military commander of Thessaloniki, martyred under the Emperor Maximian at the beginning of the fourth century. Imprisoned for openly teaching the faith, he blessed the young Nestor, who defeated the gladiator Lyaios in the arena; for this Demetrios was run through with spears in his prison.
Name days: Dimitrios, Dimitris, Dimitri, Mimis, Takis, Demetrius, Demetrios, Jimmy, Dmitri, Dmitry, Mitsos, Jim, Demetris, Dimitra, Demetra, Dimitroula, Mimi, Demi
Also celebrating on October 26
These names share the feast, many of them other forms of the same name:
Dimitrios, Dimitris, Dimitri, Mimis, Takis, Demetrius, Demetrios, Jimmy, Dmitri, Dmitry, Mitsos, Jim, Demetris, Dimitra, Demetra, Dimitroula, Demi
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.