According to the Cornell Lab of Ornithology, the name is Canada Goose.
The big, black-necked Canada Goose with its signature white chinstrap
mark is a familiar and widespread bird of fields and parks.
Many of them are not even Canadian, having emigrated permanently south to the lower-48.
Thousands of “honkers” migrate north and south each year, filling the
sky with long V-formations. But as lawns have proliferated, more and
more of these grassland-adapted birds are staying put in urban and
suburban areas year-round, where some people regard them as pests.
However, nothing is ever simple. The Latin name is Branta Canadensis, which, if I remember my long ago Latin correctly, is Goose of Canada, or Canadian Goose.
Moreover, according to Cornell:
At least 11 subspecies of Canada Goose have been recognized, although
only a couple are distinctive. In general, the geese get smaller as
you move northward, and darker as you go westward. The four smallest
forms are now considered a different species: the Cackling Goose.
This article consistently calls them the Canada Goose, and never once Canadian Geese.
Avibase, the World Bird Database, is an excellent source for all the subspecies of the Canada Goose. It has a taxonomic breakdown of the entire Branta species group. Following the links leads to specific information about each variety. It also lists synonyms in virtually every well-known language. Everything is cross-referenced and linked to the various ornithologists from which the information originates. (Note that even some of the geese specifically native to Canada, such as the Vancouver Goose, are still called Canada Geese, not Canadian Geese.)
This 10-page document from 1951, published by the American Museaum of Natural History in the City of New York is a study of the taxonomy of Canada Geese with a lot of interesting scientific information.
So, people with PhDs in ornithology call them the Canada Goose. But what do people without PhDs call them? One example: Nordstrom's sells an outerwear brand called Canada Goose.
Languagehat.com claims, without offering proof:
The vast majority of English speaking people call the goose that is
large and has a black head -— Branta Canadensis -— a Canadian Goose.
However, its original name was a CANADA Goose.....
However, the data from N-grams contradicts Languagehat. Canada goose is more frequently cited, according to N-grams than Canadian goose, and always has been. The data for Canadian geese is more complex, with Canadian geese dominating ca 1840, and currently on the upswing. According to N-grams, Canada goose dominates over Canadian goose and Canada geese dominates over Canadian geese. Thanks to @Alan Munn for the N-grams link.
Conclusion, from these and other references on Google:
Canada Goose is prescriptively correct. However, "west of the Atlantic" is a big area, with many local terms and dialects and filled with people who do not care what PhDs in ornithology or English say. If enough of them eventually say Canadian Goose, then that might become a "correct" term too.
For TGO, I recommend we stay with the terminology of Cornell, the Audubon Society, all the other ornithological experts, and Nordstrom's, and follow N-grams and say Canada Goose.
Footnote: There is also the Canada Lynx, which currently is doing fairly well in the U.S., although that might change. (There is a gorgeous pic in the link.)