The 'Mido' was to derive from his nickname of 'Mido Kanpaku' (emperor's chief advisor) when he established Hojo-ji Temple (however, he never became a Kanpaku).
「御堂」とは、彼が法成寺を創建して「御堂関白」の異名を得ていたことに由来する（ただし、実際に関白には就任していない）。