FYI: Having an Irish name has nothing to do with ending up on the list. I not only have such a name, but one that is recognizable for being associated with a very famous "republican martyr", and neither I nor any of my US family have ever been on the list. Believe me, if they were looking for folks whose names match those of accused IRA terrorists, we would be on it.
The key is that the names on the list are common ones, and thanks to the Irish diaspora, there are a LOT of Irish names that are common in the US. (My name is very strongly associated with the IRA, but it is also a really uncommon name.) Men also tend to end up on the list more often than women do because there is a shorter list of common male names than female ones.
Helpful tips: Use a shortened or lengthened form of the name. Ex.: If "James Murphy" gets flagged, next time make the reservation in the name "James M. Murphy" or "James Martin Murphy" or "James Martin Murphy, Jr.", or "J. Martin Murphy, Jr." (They won't tell you in advance if a certain form of name is on the list; you have to just guess and hope for the best.)
Most importantly, in the case of an adult who matches the list used by SWA, next time don't make joint reservations for an entire party including that person. If Dad matches the list, make a separate reservation for Dad. That way everyone else can check in online without tripping the security flag.