As so many times in Basque place- and person-names, this name of worship (San Adrian) has gone through a mutation arguably brought about by scribes and people ignorant of Basque.
Curiously enough, Saint Adrian does not hold a representative position among Basque religious icons, as opposed to the ubiquitous San Martin, San Miguel or San Juan/Donibane, but Saint Adrian was actually much revered in the ways of St James.