MD80 CREW TAXIED ACROSS ACTIVE RWY AFTER ACKNOWLEDGING CLRNC MEANT FOR ANOTHER ACFT WITH SIMILAR FLT NUMBER.

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AFTER LNDG AT DFW ON RWY 36L; WE WERE INSTRUCTED BY TWR TO HOLD SHORT OF RWY 36R AT TXWY WK. WE COMPLIED WHILE WAITING TO TAXI IN TO THE TXWY B CONCOURSE AT SPOT Z. SHORTLY AFTER TWR SAID; 'ACFT X SPOT Z; TAXI TXWY W TO TXWY G.' WE REPLIED; 'ROGER; ACFT X; TAXI TXWY WK; TXWY G TO SPOT Z.' AS WE CROSSED THE RWY; THE TWR CTLR INFORMED US WE HAD NOT BEEN CLRED TO CROSS. WE REPLIED WE HAD JUST RECEIVED AND ACKNOWLEDGED TAXI INSTRUCTIONS FROM HIM. HE STATED THOSE INSTRUCTIONS WERE FOR ACFT Y; TAXIING OUT FROM SPOT Z AT TXWY WK; WHO HE HAD SPOKEN TO ON THE GND FREQ ON WHICH HE WAS SIMULCASTING. THE COPLT AND I WERE BOTH QUITE CERTAIN HE HAD ISSUED THE TAXI INSTRUCTIONS TO 'ACFT X' (NOT ACFT Y); BUT WOULD HAVE TO REVIEW THE TAPES TO VERIFY SUCH. THE MAIN PROB HERE WAS THE MISTAKEN COMS -- EITHER ON THE PART OF THE CTLR OR THE CREW; COUPLED WITH THE FACT THE CTLR WAS TALKING TO 2 ACFT WITH ALMOST IDENTICAL CALL SIGNS; WITHOUT EITHER ACFT KNOWING OF THE OTHER. IN EITHER CASE; THE CTLR APPARENTLY DID NOT WANT US TO CROSS THE RWY AT THAT TIME. SUPPLEMENTAL INFO FROM ACN 434569: CONTACTED RAMP ON COMPANY FREQ. RETURNED TO #1 COM IN TIME TO HEAR 'ACFT X' WITH TAXI CLRNC. I WENT TO KEY MIKE; BUT CAPT HAD ALREADY BEGUN TO READ BACK CLRNC. I HEARD CORRECT READBACK AND NO RESPONSE FROM TWR.