Mamas’s name day is September 2, the feast of Mamas.
Churches that follow the Old (Julian) Calendar keep the same feast on September 15 of the civil calendar. See everything commemorated on September 2.
The saint behind the name

Mamas
September 2, Martyr, Μάμας
St. Mamas was a young shepherd of Caesarea in Cappadocia, born to parents who had themselves suffered imprisonment for Christ. Living simply in the hills with his flock, he confessed the faith openly during the persecutions of the third century and endured torture and death rather than deny his Lord.
Also celebrating on September 2
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.