HCF Controller reported when one aircraft called for departure; he heard a different callsign. When the aircraft was airborne; the error was detected as it was a different departure airport.

Narrative

Air Carrier XXX called and requested departure. Controller heard [a company] Air Carrier XYX. Controller had Air Carrier XYX on a clearance and hold for release from ZZZ1 airport. Air Carrier XXX had a clearance and hold for release from ZZZ2 airport. The Air Carrier said departing Runway 17; Controller cleared Air Carrier XYX right turn heading 350; released for departure; with a time check and a void time of XA35. A few minutes later; controller heard the Air Carrier call; and the Air Carrier asked verify the heading of 350; Controller said affirmative; then noticed that Air Carrier XYX did not tag up at ZZZ1 airport; but that Air Carrier XXX tagged up at ZZZ2 airport. Controller called Radar; and instructed Air Carrier XXX to immediately turn left heading 170; then later heading 065; and then direct CLUTS; the rest of flight uneventful. Air Carrier XYX called for release a few minutes later and flight was uneventful. This happened during the mid shift. Controller should have caught the wrong call sign; and the pilot should not have accepted the release for departure; because Controller did not use his callsign.