Marietta’s name day is August 15, the feast of the Dormition of the Theotokos.
Churches that follow the Old (Julian) Calendar keep the same feast on August 28 of the civil calendar. See everything commemorated on August 15.
The saint behind the name

Dormition of the Theotokos
August 15, Great Feast, Κοίμηση της Θεοτόκου
The Great Feast of the Dormition commemorates the falling asleep of the Most Holy Theotokos. According to tradition, the Apostles were gathered from the ends of the earth to her bedside in Jerusalem, where she gave her soul into the hands of her Son; her body was laid in a tomb in Gethsemane and was found to have been taken up, for the Mother of Life was translated to life.
Name days: Panagiotis, Panayiotis, Panos, Marios, Mario, Maria, Mary, Maro, Marika, Marianna, Mariam, Marie, Panagiota, Giota, Despina, Despoina, Panayiota, Yiota, Maroula, Marietta, Mairi, Despo
Also celebrating on August 15
These names share the feast, many of them other forms of the same name:
Panagiotis, Panayiotis, Panos, Marios, Mario, Maria, Mary, Maro, Marika, Marianna, Mariam, Marie, Panagiota, Giota, Despina, Despoina, Panayiota, Yiota, Maroula, Mairi, Despo
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.