A CPR CITATION FLC DEPARTING TEB RPTS ACCEPTING A TKOF CLRNC MEANT FOR ANOTHER ACFT WITH A SIMILAR CALL SIGN.

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REACHING THE ARPT AND PREPARING FOR THE FLT; THE TRIP WAS CANCELED. WE THEN LEFT TO REPOS TO TEB. TSTMS DEVELOPED ALONG OUR RTE. UPON TAXI; OUR DEP GATE CLOSED. WE CONTINUED TO TAXI WHILE AWAITING DEP TIME ESTIMATE. UPON JOINING THE LINE FOR DEP OFF RWY 24; WE RECEIVED REROUTING INSTRUCTIONS. WHEN ASKING FOR DEP ESTIMATES; WE WERE ADVISED THAT ATC WAS WORKING ON IT. WE CONTINUED TO MOVE UP IN THE LINE FOR DEPS TILL WE WERE NEXT TO THE HOLD SHORT FOR RWY 24 NEXT TO THE RWY -- OUR DEP GATE CLOSED. I WAS THEN DOING FUEL CALCULATIONS TO DECIDE IF WE COULD STILL MAKE OUR DEST. WE ADVISED ATC THAT WE MAY HAVE TO TAXI IN AND GET FUELED IF DELAY IS LONGER. WE WERE ADVISED OUR DEP TIME SHOULD BE SOON. MY COPLT WAS MONITORING THE GATE HOLD FREQ AND I WAS MONITORING TWR. I HEARD WHAT I BELIEVED TO BE 'ACFT X PULL UP TO THE HOLD SHORT LINE; YOU'RE #1.' I ANSWERED AND PULLED TO THE HOLD SHORT LINE. THEN HE SAID 'ACFT X POS AND HOLD.' I ANSWERED AND REPOSITIONED AND HELD. THEN HE SAID 'ACFT X CLR FOR TKOF RWY 24.' I ANSWERED AND TOOK OFF. NO PROBS TILL HANDED OFF TO DEP; WHO CALLED US ACFT Y. I CORRECTED HIM WITH THE OPTIONS NUMBER WE FILED UNDER. REALIZING THERE WAS A MIX-UP; I THOUGHT THEY HAD MISTAKENLY REFILED US FOR RERTE TAIL NUMBER. I IMMEDIATELY TOLD THE CTLR WE COULD DO ANYTHING HE ADVISED US AND ONCE AT A SAFE ALT; I CALLED TEB TWR AND APOLOGIZED FOR MY MISTAKE. CONTRIBUTING FACTORS WERE FATIGUE AND POOR NOURISHMENT AND CONFUSION OVER RERTE.