The name of the settlement was changed from Sveti Jošt to Rovte pri Nazarjih in 1955. The name was changed on the basis of the 1948 Law on Names of Settlements and Designations of Squares, Streets, and Buildings as part of efforts by Slovenia's postwar communist government to remove religious elements from toponyms. The name of the settlement was changed again from Rovte pri Nazarjih to Rovt pod Menino in 1963.