When praying for non-Jews, how should one formulate the name of the sick individual if he or she has a Hebrew-derived (vernacular) name? Eg., Jack ben Rebecca vs. Ya'akov ben Rivkah?
Personally, I don't convert the name to Hebrew. It's not their name.
There are plenty of Jews whose Hebrew name is nothing like their English name (e.g., my father is Joel/Yitzchak Isaac). If someone converted his name to Hebrew it would be wrong. If they kept it English, they'd be right.
Jack's a good example since it can be Jacob, John, or Jonathan - Yaakov, Yohanan, Yonatan - or just Jack. Why choose one when they have a perfectly good name that people and G-d know them by?
Besides, there's a limit to how much you want to convert names over, right? Do you convert Paul to Shaul? Jude to Yehudit? Katherine to Reina (Yiddish)? Mary to Miriam? Seems arbitrary to me.