E145 CREW FLEW THE WRONG ACFT TO THE DEST AFTER THE COMPANY HAD THE WRONG ACFT ON THE GATE.

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ACFT #1 WAS PARKED AT THE GATE. THE ACFT WAS DE-PWRED. I PROCEEDED TO PWR UP THE ACFT. A GND FUELER CAME OVER TO THE ACFT AND FUELED IT WITHOUT MY PROMPTING (HE ASSUMED IT WAS THE HPN AIRPLANE AS WELL). AS A RESULT OF BEING UNABLE TO QUICKLY FIND AND HAVING TO PWR UP THE ACFT; WE WERE DELAYED BEYOND THE NEWLY SCHEDULED XA30Z DEP OUT OF PHL. WITH THE WX BEING POOR IN PHL; I WAS FEELING A SENSE OF URGENCY TO 'MOVE THE FLT' OR RISK BEING IN VIOLATION OF THE 16 HR DUTY TIME REG. THE GATE AGENT CAME DOWN THE JETWAY WITH PAPERWORK AND A DISPATCH RELEASE FOR THE FLT TO HPN. I CONFIRMED THE FUEL LOAD ON BOARD MATCHED THAT OF MY RELEASE AND SIGNED THE STATION COPY. I HANDED THE RELEASE AND A LOAD MANIFEST BACK TO THE AGENT (WE HAD ZERO PAX). I BLOCKED OUT AT XA50Z. WHILE CLBING OUT OF PHL; I REVIEWED THE RELEASE AGAIN AND NOTICED THAT THE DISPATCH RELEASE INDICATED THAT THE ACFT SHOULD BE ACFT #2; WHICH HAS A COMPANY CODE OF YYY. THE ACFT I WAS IN HAD A COMPANY CODE OF XXX (ACFT #1). I INFORMED DISPATCH DURING THE CLB; VIA SELCAL; OF THE DISCREPANCY; AND THEY INFORMED ME TO CONTINUE ON TO HPN. I ARRIVED IN HPN AT XB50Z AND IMMEDIATELY CALLED DISPATCH CTL AND THE REGIONAL CHIEF PLT. I HAD A DUTY OFF TIME OF XC05Z. AS A RESULT OF THE WX; I HAD A LONG DAY. I WAS TIRED AND AS A RESULT; MY JUDGEMENT AND PERCEPTIONS WERE SLOWED. THE LAST MIN CHANGE OF SCHEDULE WAS UNFORESEEN; AND I FELT I WAS OBLIGATED; SINCE IT WAS LEGAL TO CREW SCHEDULING AND DISPATCH TO COMPLETE THE FLT TO HPN OR RISK POSSIBLE QUESTIONING OR DISCIPLINARY ACTION BY MY COMPANY'S CHIEF PLT. BEING UNABLE TO QUICKLY FIND THE ACFT COMPOUNDED THE PROB. EVERYONE AT THE PHILADELPHIA STATION; CUSTOMER SVC REPS; FUELER; GND CREW; AND FLT CREW WAS UNDER THE IMPRESSION THAT IT WAS THE CORRECT ACFT (A NORMAL FLOW ROUTINE). THAT; ALONG WITH BEING TIRED; THE SENSE OF URGENCY TO MAINTAIN LEGALITY WITH THE 16 HR DUTY TIME LIMITATION AND SIMILARITY OF ACFT CODES XXX ACFT #1 VERSUS YYY ACFT #2 CONTRIBUTED TO MY FAILURE TO NOTICE THE DISCREPANCY ON THE DISPATCH RELEASE UNTIL AIRBORNE. POSSIBLE CORRECTIVE ACTIONS: OUR COMPANY FREQUENTLY SCHEDULES 14 HR TRIPS WHICH; AS A RESULT OF DELAYS; MAY BUMP UP AGAINST THE 16 HR DUTY DAY LIMIT. BY PUSHING THE DUTY/REST AND FLT TIME REGS; THE PRESSURE TO PERFORM OR FACE DISCIPLINARY ACTION; INCREASES THE POSSIBILITY OF INADVERTENT MISTAKES. CUSTOMER SVC REPS AND OPS PERSONNEL DO NOT RELY ON ACFT TAIL N-NUMBERS. THEY RELY ON COMPANY RESERVATION COMPUTER CODES (IE; XXX; YYY; ZZZ; ETC) FOR OPS. PLTS RELY MORE ON N-NUMBERS FOR NORMALLY SCHEDULED ROUTINES; CREATING CONFUSION WITH ACFT IDENT. AT MY COMPANY AS A PLT; WE ARE NOT TRAINED ON USING THE COMPANY COMPUTER SYS. AFTER 14 HRS OF DUTY; ACFT SWAPS AND LAST MIN CHANGES TO A SCHEDULE SHOULD BE MINIMIZED IN ORDER TO PREVENT THE QUESTIONING OF LEGALITY. BECAUSE OF THE LAST MIN CHANGE; I HAD TO QUICKLY AND ACCURATELY FIND OUT THE BLOCK TIME TO ENSURE I WAS LEGAL; FIND AND PREFLT THE ACFT; FUEL THE ACFT; AND BLOCK OUT AND HOPE FOR NO OTHER DELAYS IN ORDER TO MAINTAIN LEGALITY.