FLC OF AN AIRBUS A320 TOOK A DSCNT CLRNC INTENDED FOR ANOTHER COMPANY ACFT WITH A SIMILAR SOUNDING CALL SIGN RESULTING IN ARTCC CTLR INTERVENTION TO STOP THEIR DSCNT.

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WE WERE ACR X FROM MEM TO LAX; TALKING TO ZLA; FL390; ABOUT HIPPI ON J-10. WE HEARD ZLA CLR 'ACR Y; DSND TO FL310.' I ACKNOWLEDGED; 'ACR X LEAVING FL390 FOR FL310.' FO WAS FLYING; HE PUT FL310 IN THE FCU AND WE BOTH CONFIRMED. WE BEGAN A SHALLOW DSCNT. AT FL387 THE CTLR CALLED US AND SAID THE DSCNT WAS FOR 'ACR Y.' WE IMMEDIATELY BEGAN A CLB BACK TO FL390. AS WE WERE INITIATING OUR CLB THE CTLR SAID FOR US TO DSND TO FL310 AND 'THAT WOULD SOLVE THE PROB' AND LATER THANKED US FOR HELPING HIM. I RESPONDED TO ALL ATC XMISSIONS AFTER THAT WITH 'ACR X' AND THAT SEEMED TO REMOVE ANY OF THE CONFUSION ABOUT OUR CALL SIGN. WE NEVER HEARD ACR Y ON THE FREQ PREVIOUS TO THIS AND ATC DID NOT GIVE US A 'HEADS UP' ABOUT SIMILAR CALL SIGNS. ALSO I THINK ACR Y AND I BOTH STEPPED ON EACH OTHER'S READBACK OF THE CLRNC INITIALLY. CREW FATIGUE; +11 HR DUTY DAY. AFTER LNDG I CALLED OUR DISPATCH AND REQUESTED THAT A NOTE BE ADDED TO FUTURE ACR X AND ACR Y RELEASES ABOUT SIMILAR CALL SIGNS. ACR Y GOES MSP TO SAN AND ACR X MEM TO LAX. I ALSO SENT IN COMPANY AND PLT'S GROUP SAFETY RPT IDENTING THE PROB.