It's listed as a trad song on a few sites dedicated to Irish music/writing.

The key to understanding it I think is the use of 'but'. It means in this instance imo that 'I know her name, but for all of Ireland itself I would not say who she is, and that's that, Jack'. Hyperbole.

Example: "I would not desecrate money were Beauty herself the prize." (Spoken by the fictional detective Nero Wolfe (created by Rex Stout)).