Doesn't that refer to the country or the people rather than the language? Perhaps I should have been clearer in my comment;
In my experience almost no one in the Basque Country refers to the Basque language as 'Basque', it is generally referred to as Euskara, even by non-native speakers.
Well, one of my work buddies was Basque (sadly he passed away) and spoke about “vascos” all the time. He could speak Basque perfectly (even to the point of recognizing the different dialects) and he was from a small town, were Euskera es more prevalent. That’s my experience.
In my experience almost no one in the Basque Country refers to the Basque language as 'Basque', it is generally referred to as Euskara, even by non-native speakers.