ACR WDB ACCEPTED DESCENT CLRNC FOR OTHER FLT WITH SIMILAR CALL SIGN.

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ARRIVING DFW; FLYING THE BUJ #2 ARR; CLRED TO DSND AND CROSS BATON AT 9000'. REGIONAL APCH WAS CONTACTED AND WE WERE GIVEN A CLRNC TO DEPART BATON ON A 260 DEG MAGNETIC HDG. I NOTICED AT THIS TIME THE XMISSIONS FROM APCH WERE INTERMITTENT. SHORTLY AFTER I RECEIVED A BROKEN XMISSION FROM APCH FOR FLT XY (OUR FLT) TO DSND TO 5000'. I ACKNOWLEDGED THE CLRNC AND ADVISED APCH THAT THEIR XMISSION WERE BROKEN. BEFORE WE COULD LEAVE 9000' WE HEARD A CLRNC FOR COMPANY BXY TO DSND TO 5000'. AT THIS POINT WE DELAYED DSCNT TO CONFIRM OUR CLRNC; HOWEVER BEFORE WE COULD CALL FOR CONFIRMATION WE WERE CLRED TO DSND TO 8000'. THE POTENTIAL CONSEQUENCES INVOLVED IN THIS SITUATION ARE VERY SERIOUS AND OBVIOUS. THE 2 COMPANY FLTS WITH SIMILAR NUMBERS SCHEDULED CLOSE TOGETHER INTO DFW. THE INTERMITTENT XMISSIONS AND THE FAILURE OF APCH CTL TO RESPOND TO A CLRNC ACCEPTED BY ANOTHER FLT (IF INDEED THIS WAS THE CASE) COULD CONTRIBUTE TO A SERIOUS INCIDENT. I SUGGEST ONE OF THE FLTS BE RENUMBERED. ATC SHOULD ADVISE THE SIMILAR NUMBERED FLTS OF THEIR PRESENCE ON THE FREQ; AND ALL READBACKS OF CLRNCS BE MONITORED CLOSELY. IF THE TFC IS TOO HEAVY TO ACCOMMODATE THIS; THERE SHOULD BE AN IMMEDIATE REDUCTION OF TFC.