I have searched the web in vain for the song of which you speak.
But scratching the grey matter I recall something like this:_

I took my wife to Ireland,
About a year ago.
And there we had our first born,
We named him as you know.
We took him to the clergyman,
And everything went alright,
Until he asked for the baby's name,
And she shouted with all her might.

"His name is Michael Rafferty Hoolahan Doyle,
Docherty, Doran, Murphy, Moran,
Kensit Harrigan Barrigan (something)
Bond, Duke, Killarney, Burke,
Finnegan, Kenny, O'Shea,
McGregor, McGuire, McKirk, McIntyre,
McGinnis, McGillis, McGee

Not heard it for 60 yrs, but I think that's the one you seek.
Maybe someone else can fill in the blank!
Steve