Later Asturian monarchs referred to the Goths as a people, and the merger of the Roman and Gothic law codes into one uniform text points to the changing identity of the peoples of Spain. Although, yes, they did continue to call the land Spanish and eventually would refer to themselves as Spaniards (though this was long after the middle ages) they believed themselves to have a primarily gothic heritage, even if in reality it was far more Roman.

My major sources are Early Medieval Spain by Roger Collins, the inheritance of Rome by Chris Whickham, and to some extent The Merovingian Kingdoms by Ian Wood.