How did the (apparently) Basque name García become the most common surname in Spain, including in many areas that are quite far from the Basque Country?

by anschelsc

In 2014, 6.6% of Spaniards were named García. In this map it's the most common name as far south as Andalusia. But English Wikipedia [claims](https://en.wikipedia.org/wiki/Garc%C3%ADa_(surname)) it's Basque in origin. Is that true? If so, does it represent a large Basque-descended population outside the Basque Country? If not, where does this name come from?

CheetoBenitoBurrito

Same goes, by the way, for Salazar, a supposedly Basque but not too uncommon name in Galicia, Portugal and Brazil.