ZIP codes and postal designations are established at a federal level. Modifications to mailing addresses require representatives in US Congress to make the change at that level. The part of the address that matters is the ZIP Code + 4 (9 digits total), which identifies a specific address. If the current city on the address (Pensacola) is dropped, as long as the Zip Code + 4 is intact, the mail will arrive as expected.
Perdido did at one time have a contract post office. A municipality could work with government officials to establish a contract or dedicated post office. This intergovernmental conversation is much easier for a town than for local citizens alone.