ARTCC RADAR CTLR USED WRONG CALL SIGN AND CLRED AN ACR B727 TO DSND THROUGH THE ALT OF A COMPANY B727. CAPT RPTR SAW OTHER ACFT VISUALLY AND ON TCASII ABOUT THE SAME TIME THAT THE CTLR SAW THE POTENTIAL CONFLICT AND RECLRED THE RPTR'S ACFT BACK UP TO FL330. LTSS DID OCCUR.

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CTLR CLRED OUR FLT; ACR X; TO DSND TO AN ALT OCCUPIED BY ANOTHER ACFT; MOST LIKELY DUE TO CONFUSING OUR FLT NUMBER WITH THAT OF COMPANY FLT ACR Y. THE SIT AROSE ON THE SINCA ARR BTWN DUBLIN AND SINCA. OUR FLT; ACR X; WAS CRUISING AT FL330. WE WERE CLRED TO FL310; AND SHORTLY THEREAFTER; THE CTLR CLRED US TO HOLD AT SINCA AND MAINTAIN FL280. THE FO; WHO WAS FLYING; SET FL280 IN THE ALT ALERTER AT THE TIME THE CLRNC WAS GIVEN. WE WERE AT FL305; DSNDING; WHEN I NOTICED AN ACFT AT OUR 2 O'CLOCK POS; ABOUT 1 1/2 MI DISPLACED LATERALLY AND AT 1500 FT LOWER. I STARTED AN ANALYSIS OF OUR RELATIVE POS; VISUALLY AND WITH TCASII. ABOUT 10 SECONDS AFTER I SAW THE OTHER TFC; THE CTLR CALLED TO CONFIRM WE WERE AT FL310. I REPLIED; 'NEGATIVE; WE WERE CLRED TO FL280; WHICH I READ BACK; AND WE ARE IN DSCNT THROUGH FL303 NOW.' THE CTLR ISSUED AN IMMEDIATE CLB BACK TO FL310; WHICH THE FO ACCOMPLISHED SMOOTHLY AND EXPEDITIOUSLY. I RPTED HAVING THE OTHER ACFT IN SIGHT. EXTRA CARE MUST BE TAKEN WHEN ACFT WITH SIMILAR CALL SIGNS ARE OPERATING IN THE SAME AREA. THE CTLR WAS VERY BUSY; AND THIS TIME IT WAS HIS ERROR. IT WOULD HAVE BEEN NICE IF I; OR THE OTHER ACFT; HAD BEEN AWARE OF THE POTENTIAL CONFLICT THE CLRNC SET UP AT THE TIME IT WAS ISSUED; BUT THAT WAS NOT THE CASE.