Might the nation of Brazil have been named after a mythical Island in the North Atlantic? The Celtic Myth Podshow lays out the theory:

So how did the country called Brazil end up with it’s name ? One theory says that Brazil was initially colonized by people coming from Viana do Castelo (in northern Portugal), and that through the knowledge of legends from the Celts in Galicia, they would have been aware of the lost continent of Brazil. And not only Columbus, but other early explorers from England knew about the lost land of Brazil. According to”The Island of Brazil”, a contemporary account written by William of Worcester (and published in the late 18th century) recalled that when word of a “new land to the west” reached Bristol in the late 1470s this was presumed to be Brazil. In 1480, a Bristol merchant John Jay outfitted at great expense an 80-tonne ship to sail to the island of Brazil, described as “a name often given in medieval European tales to a land far to the west of Ireland”. Setting sail in July 1480 from Bristol, Jay’s ship voyaged west, intending to “traverse the seas.” But the journey ended in failure. English crews had yet to master the new methods of astronomical navigation devised in Portugal and Spain: open, oceanic voyaging – as opposed to island hopping by way of Iceland and Greenland.

In the Welsh and Cornish myths, Bresal was a High King who made his home in the Otherworld “which is sometimes called Hy- or I-Breasal in his honor”. Like in the Irish myth, “His world is visible on only one night every seven years”. Thus, it is clear that the Celts of Galicia, Cornwall, Wales, Ireland and sailors from England all knew of the legend of the lost land of Brazil. Would it then be unreasonable to assume that when Portuguese explorers reached South America they mistakenly thought they had landed on Breasal’s world and named the land they discovered “Brazil” in his honour?

A contradictory theory sets the name in a different context:

Of course, it is possible that the name of the country called Brazil is not connected with the Celtic myth – but in my opinion this theory is not convincing. In this account, the word “Brazil” is derived from the Portuguese and Spanish word “Brasil”, the name of an East Indian tree with reddish-brown wood from which a red dye was extracted. The Portuguese found a New World tree related to the Old World brasil tree when they explored what is now called Brazil, and “as a result they named the New World country after the Old World tree”.

Quite interesting.