further info on the many "Foggy Dew"s! The version recorded by John McCormack in 1913 is indeed called "The Foggy Dew" and is the same MUSIC as the song about the 1916 uprising... but it's a completely different set of LYRICS - a love song! So Charles O'Neill reused not just the music but also the title from this love song when he wrote the revolutionary version.
Here is McCormack's recording of the love song on YouTube (You don't need a blue clicky; just copy this URL and paste it into a browser.)

https://www.youtube.com/watch?v=Ddp2xivfOU4&t=52s

Unfortunately for those of us looking for copyright info, "The Foggy Dew" MUSIC in the 1840 book The Ancient Music of Ireland is a completely different melody, not the one we're talking about.

So... the revolutionary LYRICS by O'Neill are protected in IRELAND till 2033, but already public domain in the USA. As for the MUSIC, I haven't found any reference to a composer but I guess it's pretty safe to call it 'traditional'. If that turns out to be a misunderstanding, it can be rectified after the fact. Look up the case of Paul Simon and El Condor Pasa. https://en.wikipedia.org/wiki/El_C%C3%B3ndor_Pasa_(song)

As for the subject of the same title having many different melodies attached to it and a melody having several titles attached to it, Lewis Carroll had this to say in THROUGH THE LOOKING GLASS:

[knight] The name of the song is called "HADDOCKS' EYES."'
 
'Oh, that's the name of the song, is it?' Alice said, trying to feel interested.
 
'No, you don't understand,' the Knight said, looking a little vexed. 'That's what the name is CALLED. The name really IS "THE AGED AGED MAN."'
 
'Then I ought to have said "That's what the SONG is called"?' Alice corrected herself.
 
'No, you oughtn't: that's quite another thing! The SONG is called "WAYS AND MEANS": but that's only what it's CALLED, you know!'
 
'Well, what IS the song, then?' said Alice, who was by this time completely bewildered.
 
'I was coming to that,' the Knight said. 'The song really IS "A-SITTING ON A GATE": and the tune's my own invention.'
 
-- Lewis Carroll, Through the Looking Glass