Jeremy’s name day is May 1, the feast of Jeremiah the Prophet.
Churches that follow the Old (Julian) Calendar keep the same feast on May 14 of the civil calendar. See everything commemorated on May 1.
The saint behind the name

Jeremiah the Prophet
May 1, Prophet, Ιερεμίας
The Holy Prophet Jeremiah lived in Jerusalem in the seventh and sixth centuries before Christ. Called by God from his youth, he warned the people of Judah of the coming destruction of the city for their unfaithfulness, and wept over its fall in his Lamentations. His words were often rejected, and he suffered imprisonment for speaking the truth; tradition holds that he ended his life in Egypt.
Also celebrating on May 1
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.