The modern name Britain grew out of “Prydein” – the old Welsh term for the island, which sounds like “Britain” when pronounced.
According to Welsh legend, the island was called Myrddin’s Precinct until it was settled, after which it became known as the Island of Honey.
Coming from Cornwall following the death of Porrex, Prydein, son of Aedd the Great, conquered the Island of Honey and it was renamed in his honor.
Source
Triads of the Island of Britain (Welsh ”Triads”) | 11th century to 14th century