Donyu the 3rd and the leaders following Donyu the 3rd are given a name called Nyudo-go (nyudo: lay-monk, go: pseudonym) which includes the Kanji of "入" (Nyu) when they are retired.
3代・道入以降の各当主には隠居した時に「入」の字を含む入道号という名前が贈られる。