I've never seen a map that didn't have the counties listed. Must be a cheap map if it doesn't. Official sate maps are good ones. You can often get them at the state line rest station. (At least for the states around me)
I just checked my free State Farm Road Atlas and it has the counties listed.
I have a weather radio with alert alarm in my RV. I sleep with it set on alert so if a storm is near the alarm goes off. The radio does not need to be turned on for the alarm to go off.
If you get a good weather radio they have something called SAME built into them. In that case the alarm only goes off when it is for your area and not for surrounding areas. But, you would need to know where you are to program it into the radio.