They may only have a surname, or perhaps a local name or two passed through the centuries. Many of the official Irish records were destroyed in a fire around 1920, which makes a genealogical search even more difficult. But don't despair. Help is at hand. If you have a surname, you may get help from books on Irish surnames.
Many names are specific to a few counties.
For example, the Cribbin surname has very specific links to a small town in county Mayo. Other names have clear links with the South of the Country because of their Norman origin. This kind of information is a good start to limiting your search area. Another very useful source of information is the townland or topographical index. This is not widely available, but the Ordnance Survey and the National Library would have copies which they can look up if you write to them.