I have compiled a quick Guide To Setting Up As A Sole Trader in Ireland.
Also note: Unlike in the UK where you can just trade under a business name without registering that name (IE: John Murphy T/a Murphy Builders). In Ireland you must register any business name you trade under (even if a sole trader), unless that name IS YOUR NAME – IE:
A builder called “John Murphy” could trade under the name of “Murphy” “John Murphy” or “J Murphy” without registering this business name. Should he wish to trade as “XYZ Builders” or even “Murphy Builders” he would be required to register the business name. See more here: Business name registration in Ireland