"This scheme is focussed on large-scale, cyclonic windstorms with potential for significant land-based wind impacts – often systems which develop rapidly and/or move quickly towards us; this means that all severe wind events giving rise to status Orange or status Red weather warnings will be named."- Met Éireann website
The word storm technically means wind events with an average speed of 89 to 102 km/h. However, any event with harsh enough wind effects will be granted a name.
(All info received from the met Éireann website)