What was the name of the school Socrates founded?

Socrates did not found a school in the institutional sense. His discourses, debates and arguments were conducted in the market place, temple courtyard and friends' houses. But Socrates and his long line of student generations Plato, Aristotle, Alexander, Anaximander....who followed and further developed his theories are collectively called the Socratic school of thought. Plato founded an educational institution which he termed The Academy and Aristotle founded his own which he called The Lyceum.