The toponym comes from the moat that surrounded the castle for defensive purposes. The morphology of the terrain consisted of a ditch at the foot of the small hill on which the castle stood, running from west to east along what is now Via Pizzofalcone.

The name of Piazza Fosso remained unchanged until 1932, when it was changed to Piazza Principe di Piemonte in honour of Umberto di Savoia (the future Umberto II, the “King of May”), who passed through Badolato in May 1932 to visit the family of the Marquis of France. Badolato was not the destination of the princes, but they passed through because the S.S. 106, then under construction, was still accessible from Badolato Marina.

After the referendum of 2 June 1946, with the departure of the House of Savoy, the square was renamed Fosso.

In one corner there is one of the two existing marble monuments in Badolato, dedicated to Antonio Tropeano (1865 – 1949), a doctor who was close to the people of Badolato. He was a health officer for some time and was well known and respected in the province.