Ellen’s name day is May 21, the feast of Constantine and Helen.
Churches that follow the Old (Julian) Calendar keep the same feast on June 3 of the civil calendar. See everything commemorated on May 21.
The saint behind the name

Constantine and Helen
May 21, Great Feast, Κωνσταντίνος και Ελένη
St. Constantine the Great, Equal-to-the-Apostles, was the first Roman Emperor to embrace Christianity. After his vision of the Cross and his victory under its sign, he ended the persecutions with the Edict of Milan, convened the First Ecumenical Council at Nicaea, and founded Constantinople as a Christian capital. His mother, St. Helen, traveled in old age to the Holy Land, where according to tradition she found the Precious Cross of the Lord and built churches on the holy sites.
Name days: Konstantinos, Kostas, Kostis, Dinos, Konstandinos, Constantine, Costas, Costa, Gus, Konstantin, Eleni, Elena, Helen, Elli, Lena, Heleni, Konstantina, Constantina, Dina, Ntina, Kostoula, Helena, Ellen, Elenitsa, Nitsa, Lenio
Also celebrating on May 21
These names share the feast, many of them other forms of the same name:
Konstantinos, Kostas, Kostis, Dinos, Konstandinos, Constantine, Costas, Costa, Gus, Konstantin, Eleni, Elena, Helen, Elli, Lena, Heleni, Konstantina, Constantina, Dina, Ntina, Kostoula, Helena, Elenitsa, Nitsa, Lenio
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.