Nope. Ireland has a constitution as its fundamental law, the Republic Act does not amend the constitution. It was a simply a response to provocation by Canadian orange men on a state visit to Canada and to clear up issues relating to the Lord lieutenant (IIRC on that part.) The declaration of the Republic in 16 was superceded by the 27 and 33 constitutions. It has no real legal standing (technically precedent established under the alternative courts system established following this are still valid but, not really.).
The real reason for its usage and proliferation isthe BBC style guide that the English military intelligence “influenced” - using the real name of the state would have been acknowledging the validity of our constitution which, prior to the good Friday agreement claimed the whole island of Ireland.
Teh Wikis, despite efforts to fix it up (UCC law faculty basically took it over to try and sort it out) is unfixably fucked on Irish law. The editor was originally someone who had never studied Irish law and insisted on imposing an English legal perspective on it. The state cannot be given its actual name on it. To be fair they did at least get a link to the constitution on it. Which is almost a pity as it used to be a better resource for showing how even seemingly respectable sources on the web were actually total bullshit.