Thanks. I found it there - otherwise, I couldn't have given the details above - but that's the name of the country's soccer team. The country's name is Ireland and that's what appears on my passport and in any official documents produced in any country in the world.

Apparently "Republic of Ireland" is officially the description but not the name of the state: https://en.wikipedia.org/wiki/Names_of_the_Irish_state

I guess it's similar to Germany being the "Federal Republic of Germany", or China being either the "People's Republic of China" (mainland) or the "Republic of China" (Taiwan).