Davening for someone who is sick

Rabbi, The mother of a friend of mine is very sick. I want to be able to daven for her, but when I asked my friend for her mother’s mother’s name she didn’t tell me, saying that she didn’t know what it is. I don’t want to press her because she has not discussed her mother’s illness with me beyond telling me that she her mother has pancreatic cancer. I don’t want to bring up a subject that she is obviously reluctant to talk about. Also, she is not very frum and doesn’t see a value in davening (I don’t know if that should make a difference, but I think it does). So I guess my question is - how do I daven for someone without using her mother’s name? Thus far, I have been using ’bat Sarah Imoteinu’ as a replacement, but I don’t know if that is correct. Thanks so much for your help.

Shalom I first want to wish your friends' mother a Refuah Shleima. Yes – you got it right – Bat Sarah Imeinu is the correct form You can also try finding out her name from the shule they go to – if they do Kol Tuv