Date: 201511
Local time of day: 0601-1200
Location: ZZZZ.Airport, FO
Weather elements / visibility: 10
Aircraft: Learjet 45
Operator: Corporate
Operating under: Part 91
Flight plan: IFR
Mission: Personal
Flight phase: Descent
Airspace: Class C ZZZZ
ATC / advisory: TRACON ZZZZ
Reporter organization: Corporate
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor; Flight Crew Multiengine
Human factors: Communication Breakdown
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Air Traffic Control
When detected: In-flight
Result: Air Traffic Control Provided Assistance; Flight Crew Became Reoriented
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: En route on a part 91 flight; when checking on with the Approach Controller; the Second In Command (SIC) Pilot Not Flying (PNF) used our call sign however the approach controller responded with 'November Sierra Hotel; 24R; ATIS Lima'. (Our call sign for filing flight plans is listed [with call sign but added information] in the remarks section of the flight plan for clarification to ATC.) I recall my mind momentarily dwelling on the fact that the controller was referring to our call sign like a normal 'N' number and asked the SIC to correct the controller because we may miss a radio call under those circumstances. A moment later the SIC had the opportunity to clarify our call sign with the approach controller when we were issued a descent; however it turns out; that we both actually missed the runway assignment in that first transmission from the approach controller. We had previously set up for the RWY23 transition which is most practical given the location of the FBO is nearest runway 23 and has always been the runway assignment on previous trips into [arrival airport]. The arrival has two transitions; one for runway 23; and another for runway 24L/R. We were set up; briefed; and flying the runway 23 transition and a couple miles after the turn toward the runway 23 transition side we were issued a 120 heading by the approach controller with no further information at that time. While making the turn to the 120 heading I discussed the need to query the controller for her intentions with us when the controller asked us to verify we were set up for RWY24R? We replied that we were set up for 23... which is when we realized that we may have missed something important.After arriving at the FBO we checked the arrival tape on [the internet]; and to our dismay; as we listened to our original check on transmission we heard the approach controller respond with; 'November Sierra Hotel 4; 24R; ATIS Lima'; however the SIC read back 'We have Lima; [call sign]' and missed the '24R' runway assignment read back (as did I) which lead us to initiate the 23 arrival transition. We since discussed that the mental distraction by the approach controller treating our call sign like an 'N' number must have caused both of us to miss the runway assignment. I can't actually point to anything major to correct; except to merely stress the importance of full read backs of all clearances - yet the fact remains that we both missed the same information from the approach controller and initiated a turn to the runway 23 transition when our actual clearance was to the 24L/R transition.




Synopsis: A corporate pilot reported a heading deviation caused by miscommunication with ATC when runway information was provided along with the unusual use of call sign information translated into an aircraft registration 'N' number.