The term Canada is derived from the St. Lawrence Iroquoian word 'kanata' meaning village. French explorer Jacques Cartier erroneously applied it to the entire region and the Rivière de Canada (the Saint Lawrence River). Of the many, many misunderstandings that would result between Europeans and the various tribes of North American this probably counts as the most benign.
After the arrival of the Loyalists it became expedient to divide the colony in 1791. Since Canada was still the name of the region the two new colonies were called Upper and Lower Canada.
When Confederation was being negotiated it was proposed by a delegate from either Nova Scotia or New Brunswick that the new union be called Canada. That said here are some alternative names that were proposed (many of which prove that in every age there are people who shouldn't be allowed to name things):
Anglia, Albionoria, Borealia, Cabotia, Colonia, Efisga, Hochelaga, Laurentia, Mesopelagia, New Albion, Norland, Superior, Tuponia, Transatlantica, Ursalia, Vesperia, Victorialand
This story has been questioned as the term dominion had been applied to other entities beforehand and is not innovative. Personally I feel this is an irrelevant point; conservatism done right is about looking to the past for inspiration regarding the present.
Whatever the origin the Fathers of Confederation broadened the term from being 'a major colonial possession' to being a synonym for a sovereign state. Secretary of State for the Colonies Lord Carnarvon stated in a letter to Queen Victoria: "The North American delegates are anxious that the United Provinces should be designated as the 'Dominion of Canada.' It is a new title, but intended on their part as a tribute to the Monarchical principle which they earnestly desire to uphold."
The holiday was officially renamed to 'Canada Day' in 1982 due to a somewhat embarrassing episode where there were only 12 MPs in Parliament when the voting started.
So have a happy Canada Day (or Dominion Day for the more traditionally-minded). Canada is today a spry 147 years young.
A Kisaragi Colour