ORD INBOUND ACCEPTED DESCENT CLEARANCE FOR ANOTHER AIRCRAFT; REPORTER ALLEGING AIR CARRIER'S FOUR DIGIT CALL SIGNS CREATE ADDITION CONFUSION.

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WE WERE AT FL200 ON THE PAITN 1 ARR INTO ORD. WE RECEIVED A CLRNC TO CROSS FIYER AT 9000 FT. I CHKED THE VNAV TO SEE WHAT DSCNT RATE WE WOULD NEED TO COMPLY WITH THE XING RESTR. UPON BEGINNING THE DSCNT; THE FO CONFIRMED WITH ATC THAT WE WERE CLRED TO CROSS FIYER AT 9000 FT. THE CTLR REPLIED THAT WE WERE CLRED TO CROSS FIYER AT 9000 FT. SHORTLY AFTER THE CTLR CAME BACK AND SAID THAT CLRNC WAS FOR ANOTHER ACFT; BUT TO CONTINUE TO CROSS FIYER AT 9000 FT. A FEW MINS LATER; THE CTLR CAME BACK ON; AND SAID THAT HIS SUPVR WANTED US TO CALL ATC WHEN WE GOT ON THE GND FOR AN ALTDEV; HOWEVER; IN THE CTLR'S OPINION; THERE WERE NO DEVS. I CALLED THE CTR WHEN WE ARRIVED AT THE GATE; AND HE STATED THAT HE WAS LOOKING INTO THE EVENT AND WOULD GET BACK WITH ME. THERE WERE OTHER ACR FLTS INBOUND TO ORD WITH SIMILAR FLT NUMBERS; XYWY; XWWX; AND XWXX. WE DID CONFIRM THE CLRNC AS WE BEGAN THE DSCNT; AND DON'T BELIEVE THERE WAS AN ALTDEV AT THE TIME THE CTLR CONFIRMED THE CLRNC. I BELIEVE USING THE 4 NUMBERS OF THE FLT NUMBERS HAS MADE IT EASIER TO GET CLRNCS CONFUSED; COMPARED TO WHEN WE USE ONLY THE LAST 3 NUMBERS OF THE FLT NUMBER.