The Imperial Prince of Emperor Juntoku, Prince Tadanari, was born as a son of 'Lord Jyunsanmi (Junior Third Rank) Kiyosuke,' the court lady who accompanied Emperor Jutoku to Sadoga-shima island where he was deported. Later, the background is unknown, but he went to Kyoto, and on Febuary 1247, he is thought to have secretly celebrated his attainment of manhood at the discretion of TAIRA no Tsunetaka ("Yokoki").
According to "Honcho koin jounroku" (the Emperor's family tree, made in the Muromachi period) he is said to have announced his name as 'Iwakuramiya' and 'Kogoshomiya.'
Prince Tadanari died in 1279, but his child, Takatada, is said to have later become a gon no sojo (highest ranking priest, next to a sojo) of Kajii-monzeki Temple, and announced his name as 'Iriemiya', 'Kogoshomiya', and 'Iwakuramiya' ("Kajii Enyu-bo Temple Reign Imperial Prince Den").
From the fact that both Prince Tadanari and Takatada, parent and son, announced the same reigning name, there is a view that Iwakuramiya was the first hereditary court noble, but on the other hand, the material in the Imperial Household Regency "Koshitsueidoshiryo" takes a cautious view on looking at Iwakuramiya as one of the Miyake.
It is just a guess that the origin of the reigning name 'Iwakura' and 'Kogosho' is an address or demesne (land attached to a manor and retained by the owner for their own use), and the details are unknown.