Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Tucson to Dammam as you normally would.
These are just IATA (International Air Transport Association) codes. They are used in aviation to identify and differentiate airports. That’s why a Tucson Airport to Dammam King Fahad Intl Airport flight would often be abbreviated as a TUS to DMM flight.