You are on the right track just wrong terminology.
Each fleet has a chief pilot. Each chief pilot is responsible for one fleet if it is large or several smaller fleets. The chief pilots in turn report to the Director of Flight Crew (himself a pilot).
Chief pilots tend to have served in other management roles before being appointed chief pilot eg Flight Training Manager.
As far as names go if you have a genuine reason for wanting a name then ring the switchboard, ask for the relevant fleet office and ask them (you might have to give a good reason though).