Found this web site, that shows my grandfather (definately Adrien Joseph Ducharme) as being named Joseph Adrien. I even tried e-mailing them, and they told me it's correct and they wouldn't change it. Weird?
Looks like the scan of the birth register linked to on that page has him as "Joseph Adrian", born February 10th 1895 to Jacob Ducharme and Marguerite Bedard. So perhaps that's been his real legal name all along.
I wouldn't be surprised if that's true - maybe it's an Acadian thing to not know what your legal name is :-) As an example, my father-in-law was surprised to find out (when he was around 60) that his name was spelled "Vern" on his birth certificate, not "Verne" as he had been using all his life. It caused problems when he tried to get his first passport (now that they require passports to go to Canada).