Emmanouela’s name day is December 26, the feast of the Synaxis of the Theotokos.
Churches that follow the Old (Julian) Calendar keep the same feast on January 8 of the civil calendar. See everything commemorated on December 26.
The saint behind the name

Synaxis of the Theotokos
December 26, Great Feast, Σύναξη Θεοτόκου
On the day after the Nativity of Christ, the Church gathers in synaxis to honor the Most Holy Theotokos, from whom the Saviour was born in the flesh. Having celebrated the birth of the Lord, the faithful turn with gratitude to His Mother, through whose obedience the Incarnation came to pass.
Name days: Emmanuel, Emmanouil, Manolis, Manos, Manuel, Maria, Mary, Maro, Marianna, Panagiota, Emmanouela, Emmanuela, Manuela
Also celebrating on December 26
These names share the feast, many of them other forms of the same name:
Emmanuel, Emmanouil, Manolis, Manos, Manuel, Maria, Mary, Maro, Marianna, Panagiota, Emmanuela, Manuela
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.