The reason why the family was named Mikohidari was that Nagaie, who inherited Mikosa-tei, the residence of Imperial Prince Kaneakira, Emperor Daigo's son, was called Mikosa Minbukyo (Minister of Popular Affairs in the Mikosa-tei).
家名である御子左（みこひだり）の由来については、長家が醍醐天皇の皇子兼明親王の御子左第を伝領し、御子左民部卿と呼ばれたことによる。