Lorenz’s name day is August 10, the feast of Lawrence the Archdeacon.
Churches that follow the Old (Julian) Calendar keep the same feast on August 23 of the civil calendar. See everything commemorated on August 10.
The saint behind the name

Lawrence the Archdeacon
August 10, Martyr, Λαυρέντιος
St. Lawrence was archdeacon of the Church of Rome in the third century, entrusted with her treasury and her care for the poor. In the persecution of Valerian, when the prefect demanded the treasures of the Church, Lawrence gathered the poor and the sick and presented them, saying that these were her treasures.
Name days: Lavrentios, Lawrence, Laurence, Lorenz, Lauro
Also celebrating on August 10
These names share the feast, many of them other forms of the same name:
Lavrentios, Lawrence, Laurence, Lauro
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.