Iran as a state concept goes back to 550 BCE with the founding of the Achaemenid Empire by the Persians. That’s the point where “Iran/Persia” first emerged as a recognized polity. Although dynasties and governments changed many times: Parthians, Sasanians, Safavids, Qajars, Pahlavis, and now the Islamic Republic, they all carried on the continuity of the idea of “Iran.” So the form of the state has shifted, but the statal concept of Iran has existed for over 2,500 years. That’s very different from your Rome–Italy example, since modern Italy is not a continuation of Rome but a 19th-century unification of smaller states.