Who do I contact about an incident that occurred at the gas pump?

Just go to the customer service desk...

And often there's a phone number on the pump or outside of the building....but depends on what kind of incident.

Depends on what kind of incident. Usually if the person running the station, they will put in contact w their supervisor. If its the pump Credit Card Readers you contact the fraud department. For most other complaints youd ask for the Assistant Store Director.