SIMILAR SOUNDING CALL SIGNS AND RESPONSE TO WRONG CALL SIGNS PLAGUE ATC AND THE FLC'S OF 2 CL65'S ENRTE ON FREQ WITH ZID; IN.

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OUR FLT XXY TO OMA WAS 20 NM E OF TTH VOR; CLBING TOWARD FL230 WITH MYSELF AS THE PF (AUTOPLT ON); THE FO WORKING THE RADIOS; AND NO COCKPIT CONVERSATION AT THE TIME. THEN ATC CLRED COMPANY FLT XXX DIRECT VHP VOR. WE HAD JUST PASSED VHP VOR AND IT TOOK ME A SECOND TO REALIZE ATC HAD NOT SAID OUR FLT NUMBER. ATC STOPPED SPEAKING AND OUT OF THE CORNER OF MY EYE I SAW THE FO REACHING FOR THE XMIT SWITCH. I STARTED WAVING MY HANDS AND SHAKING MY HEAD BUT MY INTERCOM WAS DESELECTED/OFF. AND BY THE TIME I GOT MY MESSAGE ACROSS; THE FO HAD COMPLETED HIS READBACK AND REALIZED HIS ERROR. I IMMEDIATELY KEYED THE MIKE AND TRIED TO EXPLAIN TO ATC WHAT HAD HAPPENED; BUT THE CTLR HAD MOVED ON TO OTHER ACFT AND THE FREQ WAS CONGESTED. ON THE THIRD ATTEMPT; I WAS SUCCESSFUL IN EXPLAINING TO ATC WHAT HAD HAPPENED; AND ALL OF THE EFFECTED PARTIES GOT THE SIT SORTED OUT. THE CTLR WAS NOT HAPPY. I CERTAINLY UNDERSTAND THE NEED FOR EVERYONE TO BE DILIGENT AND MAKE A CONCERTED EFFORT TO LISTEN CAREFULLY TO ATC WITHOUT UNNECESSARY DISTR. BUT WE WERE DOING EXACTLY THAT. I DON'T BELIEVE THIS SIT COULD HAVE BEEN MORE RIPE WITH OPPORTUNITY FOR A MISUNDERSTOOD CALL SIGN. IF THERE WAS EVER A TIME FOR ATC TO MAKE ONE OF THOSE COURTESY ANNOUNCEMENTS ON FREQ ABOUT ACFT WITH SIMILAR SOUNDING CALL SIGNS; THIS WOULD SEEM TO HAVE BEEN IT. CURIOUSLY; NEITHER ATC NOR THE OTHER ACFT APPEARED TO NOTICE THE ERROR.