The name 'Puffin' has an English history. It orginally referred to the cured carcesses of nestling shearwaters, which were a higly prised delicacy until the late 18th century, birds being mainly collected on the Isles of Scilly and Man. 'puffin' is related to 'puffling' and is a referance to the fat young birds.
The exchange of names seems to has arisen between shearwaters and puffins, which both nest in burrows. Puffin had taken its modern meaning by the late 19th century

   Fauna Britannica, Stefan Buczacki.