In my Gaelic dictionary it's spelled "deoch-an-doruis" (with hyphens), defined as "stirrup-cup, parting drink". The first name is from the idea that as you put your foot into the stirrup to ride off home, you're given a drink to fortify you against Scots weather and ghaisties etc. Note that in the verses given above, the third one ["There is a star" etc.] belongs to an entirely different song, namely "The Star o' Rabbie Burns". As for "The Parting Glass", I think it's an Irish variation on the traditional parting song of Scotland, "Goodnight and joy be wi' ye a'," which used to wind up convivial evenings before Burns wrote "Auld Lang Syne."