Hey there... yes, people do trade rain checks... most chains that offer them are national or regional, so the rain checks are good at any store within that chain. So if you get a CVS rain check and you live in PA. It will be good at my stores here in NC.
As for coupons with your name on them, yes, you may trade those too. But when you are listing them for trade, you should probably note that they have your name on them just so the other person is aware.