Breandan Breathnach in 'Folk Music & Dances of Ireland', revised edition, 1977 says of the Irish pipes:
"A plausable explaination for the name 'union' is that this [tenor] regulator and the chanter were regarded as being joined together or being in unison with each other." [This 'union happened c 1765-85.

I quote him, also, from his article 'Piper Jackson' in the journal Eigse Cheol Tire (Irish Folk Music Studies), II, p. 41, 1974-75, ".. and while we are at it, it may be no harm to point out that Walker Jackson was a performer on the union (later misnamed uilleann) pipes, but...[on to an account of Ferrar]. Breathnach, quotes two lines of a piece published Mar. 5, 1796, where one Fitzpatrick of Cork in noted to have played Union Pipes.] [Breathnach, d. 1985 or 1986, was himself an expert piper and chairman of Na Piobairi Uilleann.]

Nicolas Carolan in an article 'The Irish Bagpipes' in 'Popular Music in 18th Century Dublin', 1985, says: "Nor is it possible to say when they acquired the name of union pipes, the historically correct name.