This is called Yuhitsugaki (there were some special exceptions such as Takauji ASHIKAGA, who even let Yuhitsu write his own signature and Kao.)
これを右筆書（ゆうひつがき）と呼ぶ（もっとも、足利尊氏のように署名・花押まで右筆に任せてしまう特殊な例外もあった）。