Indeed, the toponym of Yamanouchisho, Kamakura (Yamanouchi, Kamakura City, Kanagawa Prefecture) became the basis for reading the family name of Sudo Yamanouchi clan as 'Yamanouchi.'
現に首藤山内氏が苗字の元とした鎌倉・山内庄（神奈川県鎌倉市山ノ内）の地名は「やまのうち」と訓む。