Unfortunately, not at all, because Linnaeus doesn't seem to have been in the practice of determining common names. However, you're the expert here, not me.
On the other hand, there is in fact one area where I might help. It took me a bit to track down because my library has apparently lost this particular edition (the first with birds?) though it remains catalogued, but here -- at last! -- are the pages in question from Linnaeus' tenth edition of the
Systema naturae per regna tria naturae from 1758 -- I have the full def. pictures too, if you are for some strange reason interested :
(detail from the recto)
Here we find that Linnaeus has surprisingly (at least to me) classified the animal as, I think, a duck -- "Anser". "canadensis" is still, here, a third declension adjective, so technically as a toponym it would be "of Canada", but most often translated into English as "Canadian." Someone with better Latin than me can surely correct me here, if I'm wrong.
So, in conclusion (or better, in confusion), if we're using Linnaeus as our authority (as Chic seemed to suggest with her Swedish common name point), we'd best go with "Duck of Canada".
But in all seriousness, "Canada Goose" seems to have been in print only a couple of decades after Linnaeus' tenth edition, so it's not like this was a particularly active controversy.
So, my actual professional opinion as a historian of not-birds (unlike birdman and chicbird) is that it seems that the Common Names of animals are in no way derived from literal translations of their Latin names. We just call them whatever catches on.
I'd welcome any corrections here from the bird docs or the classicists.