You poor Yankees don't know that you are talking about hat checks, not seat checks. The number on a hat check (originally stuck in the band on the passenger's hat) did identify the station number (usually the mile post for the station the passenger was going to). Some roads did have the names of stations on the checks, and the conductor would punch by the name of the destination station.
I once had occasion to help another passenger find his seat one night. I was going from Charlottesville to Ronceverte, and spent some time in the lounge car after dinner. As I was leaving to go to my seat, a soldier approached me (for some reason, he may have mistaken me for a C&O employee) and asked for help in finding his seat (he did not remember which coach he was in, either). After asking him where he was going, I was able, from the C&O timetable, to determine what number was on his hat check (I knew that the mileposts were numbered from Phoebus, not Washington), and we went through the coaches until we found his seat by looking at the hatchecks.