I think that even if the song had had a title in some Gaelic language, that English speakers would have given it a new title which sounded similar but made some sense. Whether you call it 'Parson upon Dorothy' or 'Parson upon Dolly,' it doesn't make sense, and it's just a scrap of nonsense from the past which we will probably never understand.

I have looked at many country dance tunes, and while their names may be whimsical, they all make sense. They show a modicum of good taste, too.

Recently I had occasion to search for a different, rather well-known tune on the site called TheSession. The site listed 30 known names for it. Clearly, if we spend too much time on the names of tunes, we won't have time to play them and have fun.

(Now I remember: the tune with 30 names was "The Night Larry was Stretched.")