This has been an issue for a while. With most situations, we advise businesses to create localised content when targeting different countries (in both their own language and their target markets), Northern Ireland is in a difficult position. Forgetting the political situation, Northern Ireland is part of of the .UK ccTLD group. This includes co.uk, .com.uk, .org.uk, and so on.
Ireland on the other hand has the .IE ccTLD extension, and for reasons unknown to me, doesn't have the .gov.ie, .co.ie, .org.ie subs. Which means the Governments' domain names are as exclusively recognisable as that of countries who do have a .GOV.xxx domain TLD.
Most people in Northern Ireland, with a UK/NI ISP, would have Google.co.uk (or Bing.co.uk or Yahoo.co.uk*) as their home page. Therefore their results are "localised" to UK results. Bear in mind that Belfast does have a UK Local Search (Dublin currently doesn't, at time of writing).
Thus business on either side of the border may have to consider having a .IE and a CO.UK for their business - which adds a bit of a nightmare to their content management and online Brand development.
As with .COM's, the lack of availability of domains on a global and national space is a growing problem. Many companies share the same names, and even with regional ccTLD's, the problem persists, as company names aren't always exclusive (unless protected by Trademark or other Registration). The problem is exacerbated for Northern Ireland, which is growing in it's connectivity with its neighbour to the South. There is no real border anymore, calling Northern Ireland from the South doesn't require an international extension.
The problem is, in part, that the web is still governed by a US-centric view of the world and a continued lack/resistance to localise, due in part to the pervasive myth that having a .COM (or indeed any TLD) is going to make your business global. Worse is the frightening trend that many Web design companies-cum-online marketing types still sell .IE domains only to companies clearly targeting other countries.
Its for this reason that I've never been a big promoter of the .EU domain. I just don't get it's point. Its no more relevant to someone in France or Ireland or Italy than any other domain bar their own. Given the different population and area sizes of some countries - and their own regional independence questions, perhaps the .EU needs to be localised. :-). The .IE covers a much smaller population than do .FR, .IT and .DE - so their localisation issues are probably much greater.
Thank you to @IvanODonoghue who pointed out that Scotland and Wales are probably in a similar predicament, as are maybe other ethnic groups living as part of a wider national
*Yahoo however, includes .CO.UK as potential Irish matches, particularly if hosted in Ireland