The thought just occurred to me (entirely unburdened by knowledge): could the line "For Ireland I'd not tell her name", be an archaic variation of something like "For the life of me, I don't know her name", or something like that?

When I used to see this title (never saw the words of the song), I supposed that the title meant something like "My loyalty to Ireland is greater than my loyalty to her", or else vice versa. But now I'm thinking that "She's the most wonderful creature who ever walked the Earth, but, gosh darn it, I don't know her name!" is a more likely interpretation.

Those with actual knowledge of the song should jump right in!

Don