While being a high priest, Shunyu had firmly declined offers for the various positions but was known as Naiku and was also referred to as Ishiyama Naiku or Fugen-in Naiku.
高僧でありながら、諸職を固辞していた淳祐がこの内供を称され、「石山内供」「普賢院内供」とも呼ばれている。