FLC OF AN LTT CARGO JET RESPONDED TO ANOTHER SIMILAR SOUNDING CALL SIGN AND CLBED FROM ASSIGNED ALT.

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ENRTE FROM MONTREAL; CANADA; TO WILMINGTON; OH; CHARTER X CHKED IN WITH ZBW AND THEY CLRED US TO FL350. THEY THEN AMENDED THE CLB TO FL260. CLBING THROUGH FL245; BOTH MY FO AND I HEARD; 'CHARTER X CLRED TO FL350.' THE FO READ BACK 'CHARTER X CLRED TO FL350.' NOTHING FURTHER WAS HEARD. CLBING THROUGH FL285; ZBW ASKED FOR OUR ALT. THE FO REPLIED AND WE HEARD ZBW ADVISE SOME OTHER ACFT THAT 'THE TFC IS ABOVE YOU NOW.' ZBW THEN ASKED US IF WE REMEMBERED OUR CLB BEING AMENDED TO FL260. THE FO REPLIED 'YES; BUT THEN WE WERE RECLRED TO FL350.' ZBW THEN TOLD US THAT THAT CALL WAS FOR COMPANY CHARTER Y. WE HAD NOT HEARD COMPANY ON FREQ. BOTH OF US HEARD FL350 FOR CHARTER X AND CHARTER X DEFINITELY READ BACK FL350. DURING THIS DISCUSSION; WE OBSERVED TFC PASS TO OUR R; APPROX 150 DEG HDG DIFFERENCE; APPROX 2000 FT BELOW OUR ALT. I ASSUME THAT ACFT LIKELY HAD A TCASII INDICATION AND THAT 10 NM SEPARATION MAY HAVE BEEN BROKEN. AFTER OUR ORIGINAL FL260 RESTR; ZBW RPTED OUR TFC AS NBOUND (OUR HDG WAS 235 DEGS) AT OUR 9 O'CLOCK. IF THAT WAS THE POS OF OUR TFC; WHEN WE HEARD OUR CLRNC TO FL350; IT MADE SENSE AS THAT TFC WOULD HAVE BEEN BEHIND US AT THAT POINT. THIS INCIDENT MAY HAVE BEEN AVOIDED IF ZBW HAD ADVISED US THAT COMPANY CHARTER FLT WAS ON FREQ AND MORE IMPORTANTLY IT WOULD HAVE BEEN AVOIDED IF THEY HAD REACTED TO OUR READBACK OF FL350. THE RESULTING LOSS OF SEPARATION DID NOT RESULT IN A CONFLICT; BUT THE POTENTIAL WAS THERE.