I looked up the Registration of Business Names Act 1963. Section 3 says that:
6.—(1) The particulars required to be furnished under this Act by any person shall be furnished within one month after his adoption of the business name.
6.—(2) If the person has adopted the business name before the commencement of this Act. the particulars shall, if not already furnished under the repealed enactment, be furnished within one month from the commencement of this Act.
6.—(3) This section shall apply, where registration is required in consequence of a change of name, as if for references to the date of adoption of the business name there were substituted references to the date of such change.
It doesn't say that failure to register the name is an offence.
Then section 8 says this:
8.—(1) On receiving a statement under section 4, or a statement under section 7 specifying a change in the business name, the registrar shall send by post or deliver a certificate of the registration thereof to the person registering.
8.—(2) A certificate of registration shall be kept exhibited in a conspicuous position at, in the case of a firm or individual, the principal place of business and, in the case of a body corporate, its registered or principal office in the State and, in every case, in every branch office or place where the business is normally carried on, and if not kept so exhibited, the person registered or, in the case of a firm, every partner in the firm shall be liable on summary conviction to a fine not exceeding £100.
So am I reading this right? It's an offence not to display a certificate once you have it, but it's not an offence not to get one within the one month time period?
The full text of the act is here:
http://www.irishstatutebook.ie/1963/en/act/pub/0030/print.html
There are a load of Business Name Regulations as well but they appear to only deal with the fees to be paid for the various certificates etc.
ETA - I found this article too but from what I can find on the Irish Statute Book website these changes were never implemented? I can't find the this Registration and Display of Business Names Bill 2000 anywhere on the Dáil website. Article is here: