I know this won't help you now but may in the future. I assigned each invitation a number. On my guest list, I had a number next to the invitee's name/s. I wrote this number in pencil on the back of the invitation way down in the bottom corner. I was then able to know whose invite it was when it came back w/o a name, which I also had a few of.
But that doesn't help you now, does it? lol If you are having place cards, you will need their names. Maybe you will receive the responses from the other guests from the same city and be able to figure out who it is by process of elimination. If not, then you will probably have to call. If they didn't include the number attending, you probably will also need to call. How do people make something so difficult that should be so simple??