A B737 CREW HAD SIMILAR CALL SIGN MIX-UP WITH COMPANY FLT IN ZDC CLASS A AIRSPACE.

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ANOTHER ACR FLT WITH SIMILAR CALL SIGN WAS NAVING AHEAD OF US ON SAME CTR FREQ. THE OTHER ACR FLT HAD ANSWERED FOR US AT LEAST TWICE. I HAD REQUESTED FL350; BUT WAS TOLD IT WOULD BE A FEW MINS. I THOUGHT I HEARD A CALL FOR THE SIMILAR SOUNDING (IE; 1 NUMBER OFF) ACR FLT TO CLB TO FL350. THE OTHER FLT ANSWERED THE CALL AND CTR DID NOT CORRECT CALL SIGN. MY FO VERIFIED IT WAS FOR THE OTHER FLT. THEN I HEARD CTR TELLING THE OTHER ACR FLT TO REMAIN AT FL310! OUR FLT NUMBER WAS NOT CALLED. A FEW MINS LATER; I QUERIED CTR JUST TO ENSURE THAT WE HAD NOT BEEN THE ONES CLRED TO FL350 (EG; I SAID 'ACR XXXX STILL AT FL310; CAN WE EXPECT FL350 SOON?' OR SOMETHING VERY CLOSE). CTR THEN CLRED US TO CLB TO FL350. AFTER THINKING ABOUT THIS SCENARIO; I COULD NOT BE 100% SURE IF WE HAD NOT MISSED THE CALL TAKEN BY THE OTHER ACR FLT. IF SO; OUR CLB TO FL350 FROM FL310 WAS DELAYED BY A FEW MINS DUE TO THE CONFUSION. WHEN ARE WE GOING TO SOLVE THESE TYPES OF HUMAN COM PROBS WITH SOME SORT OF DATA LINK/WRITTEN COM? THE HUMAN EAR(S) IS JUST TOO FALLIBLE!