It was named, at least indirectly, after the first settler in the Little River Valley, David Canada, whose father Daniel purchased land there in 1709 after first arriving in Canterbury and being disappointed that land speculators had already bought up the best land in the Quinebaug Valley went west over the next ridge.
Canada always seemed as an odd last name.
Then I was reading Early homesteads of Pomfret and Hampton and saw this:
in the vernacular of the times they named the settlement "Kennedy" in honor of David Canada,
That raised an eyebrow and a check of the etymology of Kennedy:
Kennedy is an Anglicised form of Cinnéidigh,
In a time well before standardized spelling, Canada pronounced as Cinnéidigh (or Canaday) rather than as the Iroquoian word Kanata that named the nation to our north makes sense.