When we pray for the healing (refuah) of a woman or girl, we refer to her as "(patient's name) bat (patient's mother's name)", for example "Shoshana bat Michal" or "Rivka bat Shifra Aviva". This is according to the template of the Mi Sheberach "Prayer For A Sick Person" (Siddur, Ahavas Shalom - The Complete ArtScroll Siddur, Nusach Ashkenaz, Rabbi Nosson Scherman, Mesorah Publications Ltd., 1984).
However, after a woman gives birth, we pray for her as "(new mother's name) bat (her-father's-name)". This is according to the template of the Mi Sheberach "Prayer For Mother And Newborn Child (And Naming A Baby Girl)" (ibid).
What's up with that?