I have seen a copy of a Mi’sheberach for cholim that in addition to the names of Avraham, Yitzchak, Yaakov, Moshe, Aharon, David and Shlomo also adds the names of Sarah, Rivka, Rachael and Leah. When was this Mi’sheberach created? If when we say a prayer for cholim, we use the mothers name, is it appropriate to add them to the Mi’sheberach? Why were they not included? Who was the author of it? Thank you for your advice.

Shu"t Avkat Rochel (13) refers to the nusachim of the MisheBeyrach as a custom set by the community. Siddur Olat R'iiyah of HaRav Kook does refer to the Matriarchs in the MisheBeyrach for the sick. As you point out, the sick person is called by his name and the name of his mother- this based on the Zohar (see Shu"t Daat Cohen 132).