Aimilanos’s name day is July 18, the feast of Emilian of Dorostolum.
Churches that follow the Old (Julian) Calendar keep the same feast on July 31 of the civil calendar. See everything commemorated on July 18.
The saint behind the name

Emilian of Dorostolum
July 18, Martyr, Αιμιλιανός
St. Emilian was a Christian of Dorostolon on the Danube who suffered martyrdom in the fourth century, in the reign of Julian the Apostate. Moved by zeal for the true God, he entered a pagan temple and overturned the idols; when another man was blamed for the deed, he came forward and confessed it freely rather than let the innocent suffer.
Also celebrating on July 18
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.