Answer:
No-one knows exactly. The name "Britain" originates from the Romans, who conquered much of the island of Great Britain (which includes present day England, Scotland and Wales). They called the local Celtic tribes the "Britanni".
Later, the Romans left and German tribes invaded the island, such as the Angles and the Saxons (the Angles gave the name "England"). Some of the Britanni stayed on the island, which became Great Britain, and a smaller number escaped to France. The region of France they settled in became known as Lesser Britain. Today the English call this region "Brittany". The French call it "Bretagne" and call Great Britain "Grande Bretagne".