This is totally incorrect. The Irish Free State / Saorstát Éireann was established on 6 December 1922 by the Irish Free State Constitution Act of 1922 (UK) and the Constitution of the Irish Free State (Saorstát Eireann) Act 1922 (Dáil Éireann), subsequent to the Anglo-Irish Treaty of December 1921. Following its adoption by referendum in July 1937 the new constitution Bunreacht na hÉireann came into force in December of that year. Under art 4 of the Constitution "The name of the State is Éire, or, in the English language, Ireland.". The Irish Free State came to an end with the coming into force of the new constitution which also repealed the constitution of the Irish Free State. The constitution did 'refound' the state as "a sovereign, independent, democratic state.", whereas under the previous constitution it was "a co-equal member of the Community of Nations forming the British Commonwealth of Nations.".The "Republic of Ireland" is the "Irish Free State", the name was changed in the 1940s but there was no refounding of the state.
The 'Republic of Ireland' is a football team. However, when Ireland left the British Commonwealth, the Republic of Ireland Act 1948 provided that "Ireland may be officially described as the Republic of Ireland", but it didn't change the name of the State from Éire / Ireland. So Republic of Ireland is a descriptor but not the name of the State in Irish law.