E145 ON APCH TO DFW ACCEPTS CLRNC; TURNS AND DSNDS; ISSUED TO ANOTHER ACFT WITH SIMILAR CALL SIGN.

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ON ARR INTO DFW FROM CID ON UKW 8 ARR; AN EMER AROSE AT DFW -- ACTUALLY 2 EMERS. ATC STARTED TO GET EXTREMELY BUSY AND ADVISED EVERYONE THAT 2 RWYS WERE CLOSED DUE TO THE EMERS; AND FOR EVERYONE TO EXPECT VECTORS. THE CTLR; WE THOUGHT CALLED OUR FLT NUMBER TO TURN L AND DSND FROM 11000 FT TO 5000 FT. WE STARTED OUR TURN AND DSCNT WHEN ABOUT 90 SECONDS LATER; WE WERE TOLD THE INSTRUCTIONS WERE NOT FOR US; BUT FOR ACR Y. THE PNF (CAPT) READ BACK THE INSTRUCTIONS TO DSND AND THE CTLR NEVER RESPONDED OR CORRECTED OUR ACTIONS. WE HEARD OUR NUMBER ORIGINALLY; BUT THE CALL SIGN WAS BLOCKED OUT. WE ASSUMED IT WAS FOR US. WE WERE AT 10000 FT BEFORE THE CTLR TOLD US TO CLB BACK TO 11000 FT AND TURN R TO GET BACK ON THE STAR. NO OTHER ACTION WAS TAKEN BY THE CTLR AND NO TFC CONFLICT AROSE. CONTRIBUTING FACTORS WERE THE CTLR NEVER WARNED US OF SIMILAR CALL SIGN -- WHICH IS USUALLY DONE. THE CTLR WAS WORKING MULTIPLE FREQS. WE FAILED TO CLARIFY SOMETHING WE WERE NOT COMPLETELY SURE OF; GIVEN THE ATC CTLR WAS EXTREMELY BUSY AND COULD NOT BREAK IN TO CLARIFY. FACTORS: MULTIPLE EMERS AT DFW. BLOCKED CALL SIGN. NEVER WARNED OF ACR Y ON FREQ. ATC WORKING MULTIPLE FREQS. CAPT READING BACK INSTRUCTIONS AND NEVER WAS CORRECTED. CREW FAILURE (OUR) TO CLARIFY IF NOT 100% SURE OF INSTRUCTIONS.