Medium Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Confusion; Distraction; Situational Awareness; Workload; Time Pressure
ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Flight Crew Requested ATC Assistance / Clarification
Company Policy; Human Factors
We were operating [Flight ABCD].  I had obtained my clearance via the ACARS PDC; which gave us the squawk code and flight number and assigned route.  I contacted ground using the correct call sign and ground responded with the incorrect call sign; but I did not think anything of it because it was a quick taxi and we were switched over to tower.  We had to run the Runway SID change checklist.  Tower asked us if we were ready and we responded with that we needed a few minutes to run a checklist.  I remember being confused because tower was calling us by the wrong flight number.  After running the checklist we contacted tower and told them we were ready.  The controller used the wrong flight number again and we attempted to correct him with emphasis on our flight number.  I did mention this to the Captain and he told the controller very plainly that we were [Flight ABCD].  Then the controller messed up the call sign again and cleared us for takeoff.  Once we were airborne Departure Control told us that [Flight ABCD] was not an active flight and all they had on file was a [Flight ABDD]. ATC instructed us to change our call signs and squawk code. ATC was expecting us to use the flight plan for [ABDD]; but we did not have that information because we had [ABCD] clearance.Due to this confusion we should have corrected the call sign before takeoff.
[Report narrative contained no additional information.]
There was confusion over a flight number at DCA. ATC was using one flight number and the crew had a different; similar flight number; but did not clarify ATC's mistake until after takeoff.