If you want more discussion about uillean pipes/ union pipes search this year's correspondence archives at http://listserv.hea.ie/irtrad-l.html It appears the two names are distinct from each other rather than one being a transliteration of the other, the Irish name referring to the bellows pressed by the elbow, the English-language name referring to the union of drones and chanter.
To get back to Greensleeves, a school teacher told us that it the song was about an army camp follower. Has anyone else heard that and does it make sense to you?