When can a tower's callsign differ from the airfield name, and how do I find the proper callsign?
I doubt pilots are expected to have airport diagrams handy for every airfield in the vicinity just for this.


And you're wrong to doubt that.


  If, say, I had to divert to an unfamiliar airfield, how would I find the proper callsign for its tower?


From the chart. Same place you'd get the tower frequency...