When flying from Fayetteville, North Carolina to Dothan, the time of day you decide to fly out makes little to no difference towards the overall price you’ll pay on tickets.
These are just IATA (International Air Transport Association) codes. They are used in aviation to identify and differentiate airports. That’s why a Fayetteville Airport to Dothan Arpt Airport flight would often be abbreviated as a FAY to DHN flight.