Most but not all Republics in Europe follow a pretty conventional naming style of [Nationality] Republic, like how France is officially the French Republic, or Portugal the Portuguese Republic. Ireland followed this trend during it's revolutionary period in the early 20th century, officially naming itself the Irish Republic twice, once during the Easter Rising in 1916, and again in 1919 during the First Dail (Parliament). Even when Ireland achieved only partial independence with Dominion status, it's name in Irish was Saorstát Éireann, with "Saorstát" literally translated as Free State, but more sincerely meaning Republic before the term "Poblacht" gained popularity.
Why then did in 1948 did Ireland change it's official description (not name, as that is constitutionally defined) to "Republic of Ireland" when "Irish Republic" had both historical precedent, and was the most common styling convention in Europe?
In 1916 the Irish Republic (in Irish Poblacht na hÉireann) was proclaimed during the Easter Rising. The Rising was put down within a week with many of the leaders executed and many more imprisoned. Then in January 1919 Irish candidates elected to Westminster instead met in Dublin to form Dáil Éireann and reaffirmed the Irish Republic (in Irish: Saorstát Éireann). All MPs elected from the island of Ireland were invited to Dáil Éireann but only those from Sinn Féin, the republican party, attended. They were anti-partition and saw the parliament they created as representing all 32 counties of Ireland.
In November 1921 a Treaty was negotiated with the United Kingdom giving 26 counties dominion status to be called the Irish Free State (in Irish: Saorstát Éireann). There was a near even split in Dáil Éireann, which narrowly backed the Treaty, and in July 1922 a civil war broke out. The Anti-Treaty forces, who viewed themselves as the legitimate inheritors of the Irish Republic, dumped arms in May of 1923 ending the conflict. The Free State had officially came into existence the previous December.
In 1932 Éamon de Valera, one of the political leaders of the Anti-Treaty forces, came to power with a new political party and in 1937 he wrote Bunreacht na hÉireann (Constitution of Ireland) which changed the name of the country to Ireland (in English) or Éire (in Irish). Articles 2 and 3 (revised in 1999 as part of the Good Friday Agreement) declared that Ireland is a 32 county country "pending the re-integration of the national territory".
OK, after all that prep I finally get on to the answer! De Valera was pretty happy to leave things the way they were with Ireland in the Commonwealth, saying that Ireland was "a republic in all but name" and that it didn't need to be officially declared. However he had drafted an act to declare Ireland a republic before he lost power in 1948. This may have been the act that John A. Costello introduced or he may have written up a new one.
The Irish Republic declared in 1916 and reaffirmed in 1919 was a 32 county entity. This was seen as the name reserved for a future, reunited, 32 county country and using this as the descriptor in 1949 would have been unpopular, especially within nationalist communities in Northern Ireland. It would have sounded like "the Irish Republic has been set up, job done." The Republic of Ireland highlights the republican nature of the state but hints at it acting as a placeholder until the 32 county republic envisioned in 1916 and 1919 can be established. As you mentioned the act only changed the description of the state and had very little actual impact, other than Ireland's exit the Commonwealth. Fintan O'Toole wrote a book a number of years ago called "Enough is Enough: How to Build a New Republic". He ends with 50 key actions, of which number 50 is "Declare a republic."
Interestingly, in Irish, both 'Republic of Ireland' and 'Irish Republic' are translated as 'Poblacht na hÉireann'. I have an Irish history channel on Youtube and put up an episode recently on some of the difficulties faced in translating the word republic into Irish in 1919 which is here.
TLDR: The Irish Republic is strongly associated with a 32 county state. To declare the Irish Republic in 1949 would have been unpopular and would have met with opposition from nationalists in Dáil Éireann and wider society. There is very little chance that a referendum to change the name of the nation would have passed. Changing the description to the Republic of Ireland broke Ireland out of the Commonwealth and repudiated the British monarch as Head of State without requiring a constitutional amendment or alienating or angering nationalists.