The Chida writes that when Davening for a חולה we use the mother's name.
The reason is because we need a lot of Zechusim. Usually women have more Zechusim than men. Women don't have the Aveirah of Bitul Torah.
The Steipler zt"l once Davened for Reb Yechezkel Abramsky zt"l not knowing his mothers name. He Davened for Yechezkal Ba'al Mechaber (author of) Chazon Yechezkal.