What Polish name might be pronounced "Jashuskey"?

You know, that’s not a bad guess, either. That name gets all sorts of varied renditions in English, and the OP’s name is not that far off. In Polish, it’s something like “kshih-SHEF-skee.” But in English, I hear “ker-ZOO-skee,” “chih-SHEV-skee,” “chuh-ZOO-skee,” all sorts of stuff.