Vangelio’s name day is March 25, the feast of the Annunciation.
Churches that follow the Old (Julian) Calendar keep the same feast on April 7 of the civil calendar. See everything commemorated on March 25.
The saint behind the name

Annunciation
March 25, Great Feast, Ευαγγελισμός
The Great Feast of the Annunciation commemorates the day the Archangel Gabriel was sent to the Virgin Mary in Nazareth to announce that she would conceive and bear the Son of God. Her humble acceptance as the handmaid of the Lord opened the way for the Incarnation, and at that moment the Word of God took flesh in her womb.
Name days: Evangelos, Vangelis, Vaggelis, Vagelis, Evangelis, Evangelia, Lia, Vangelitsa, Evangelina, Vangelio, Vaggelio, Evangeline
Also celebrating on March 25
These names share the feast, many of them other forms of the same name:
Evangelos, Vangelis, Vaggelis, Vagelis, Evangelis, Evangelia, Lia, Vangelitsa, Evangelina, Vaggelio, Evangeline
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.