What are the royal names of Ireland? In the modern world, there is no such thing as an Irish Royal family; however, in the past there have been many Irish names considered Royal, as well as Royal names from the English monarchy that had control over Ireland for a large period of their history.

There are actually a very limited number of royal names of Ireland and finding information on them is very difficult for several reasons explained here:
Tracing Irish genealogy to Royalty, then, requires the knowledge and information to trace lineage back past the 1600s, simply because during that time the loss of power led to the changing of names, the loss of alliances, and even the loss of written histories that would have proved reliable.
It is possible to trace a Royal family bloodline into distinct Irish history, but the level of separation between then and now is so extreme that there isn't any true connection to be made in terms of relation to original Irish Royalty.