UNAUTH TKOF ATTEMPTED AFTER ACR FO MAKES REPLY TO WRONG CALLSIGN.

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FLT WAS DEPARTING ORD TO PHL. WE WERE CLRED ONTO RWY 32L TO POS AND HOLD. AS WE COMPLETED OUR CHKLIST; WE RECEIVED CLRNC FOR TKOF. THE COPLT ROGERED OUR TKOF CLRNC; AND HE ADVANCED THE THROTTLES. ABOUT 1000 FT DOWN THE RWY; TWR TOLD US THAT WE HAD NOT BEEN CLRED FOR TKOF. I WAS PREPARING FOR A LOW SPD ABORT WHEN TWR CAME BACK AND CLRED US FOR TKOF; MAINTAIN RWY HDG. AFTER LIFTOFF WE DISCOVERED THAT TWR WAS ALSO CTLING AN ACFT ON RWY 32R. THEY BELIEVED THAT WE HAD MISUNDERSTOOD THE TKOF CLRNC ISSUED TO THE OTHER ACFT TO BE OUR OWN. THEY ALSO INFORMED US THAT THERE WAS NO TFC CONFLICT AT THAT TIME. THIS INCIDENT COULD HAVE BEEN AVOIDED IF WE HAD NOT MISUNDERSTOOD OUR CLRNC (HEARBACK ERROR). THE TWR HAD HEARD AND CORRECTED US ON OUR READBACK. IF SIMULTANEOUS DEPS FROM PARALLEL RWYS WERE ALWAYS HANDLED ON DISCRETE FREQS. SUPPLEMENTAL INFO FROM ACN 242124: SIMPLY PUT; WE EXPECTED A TKOF CLRNC; TO THE BEST OF OUR KNOWLEDGE WE RECEIVED ONE; AND WE WERE NOT CHALLENGED IN OUR READBACK. DUAL DISCRETE FREQS DURING TANDEM PARALLEL RWY OPS WITH 1 CTLR IS A RECIPE FOR CONFUSION.