When a Northern Irish athlete wins a gold medal at the Commonwealth Games...

…what song / anthem plays at the medal ceremony?

it’s “Danny Boy”

http://en.wikipedia.org/wiki/Londonderry_Air

Wikipedia says it is the Londonderry Air, which apparently is the basis of several songs, including Danny Boy.

Of course, as with just about everything else, talking about the tune can betray your affiliation - it’s the Londonderry Air, or the Derry Air, or Danny Boy, depending on who you don’t want to offend

Correct. But the name of the tune is “Londonderry Air” – named after a melody collected in the city then called Londonderry, but now Derry. Just as the famous topological puzzle called “the Seven Bridges of Konigsburg” was first set by Immanuel Kant when he lived in the city then called Konigsburg, now Kaliningrad.

The city’s offical name is still Londonderry, even though plenty of institutions (including the city council) have been renamed. And anyway, my whole point is that even when the melody was collected, plenty of people didn’t use that name.