ZOB ARTCC GETS SIMILAR SOUNDING CALL SIGNS OF 2 G200 ACFT CONFUSED.

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WE WERE IN CRUISE FLT AT FL370 ON J34 NEAR GRR (GRAND RAPIDS; MI) EBOUND TO IAD. AS IT TURNED OUT WE WERE BEHIND ANOTHER ACFT FROM OUR COMPANY WITH A SIMILAR SOUNDING CALL SIGN. WE WERE BOTH ON THE SAME FREQ WITH ZOB. OUR OTHER COMPANY ACFT WAS ENRTE ALSO. WE WERE AWARE THAT THEY WERE AHEAD OF US AND WERE CAREFUL ABOUT THE SIMILAR CALL SIGNS. UPON CHKING IN WITH ZOB WE WERE INSTRUCTED TO STAND BY. THE CTLR WAS VERY BUSY AND WE WAITED QUIETLY TO HEAR BACK FROM HIM AS HE DEALT WITH OTHER ACFT. AFTER A FEW MOMENTS THE CTLR ASKED OUR SISTER SHIP IF THEY COULD ACCEPT FL390. THEIR CREW RESPONDED WITH A STAND BY; WHILE THEY CHKED THEIR WT AND PERFORMANCE DATA. THEY SOON ANSWERED THAT THEY COULD ACCEPT FL390 AND THE CTLR THEN CLRED THEM TO CLB TO FL390 FOR XING TFC. IN THE MEANTIME IN OUR ACFT WE NOTICED ON TCAS AN ACFT AT OUR ALT OFF OUR R SIDE THAT APPEARED TO BE INTERCEPTING OUR PATH. WE SOON FELT THAT THE CTLR WAS LOOKING AT US AND YET INSTRUCTING OUR SISTER SHIP TO DO THE CLB THAT WAS REALLY MEANT FOR US. WE BROKE INTO THE CONVERSATION AND EXPLAINED TO THE CTLR THAT WE BELIEVED THAT HIS INSTRUCTION WAS BEING GIVEN TO THE WRONG ACFT; OUR SISTER SHIP AHEAD OF US. WE WERE HOPING THE CTLR WOULD CORRECT THIS ERROR AND SEND US UP TO CLR THE XING ACFT AND PERHAPS ADVISE OUR SISTER SHIP TO CANCEL THEIR INSTRUCTIONS. UNFORTUNATELY; THE CTLR BECAME MORE CONFUSED AND EXCITED AND CONTINUED TO CALL OUR SISTER SHIP TO CLB RAPIDLY AND TURN L. HE ALSO INSTRUCTED THE OTHER ACFT TO TURN AND DSND. WE NEVER HEARD THE OTHER ACFT ANSWER AND BELIEVE THAT THE CTLR WAS WORKING 2 FREQS IN HIS SECTOR. BY NOW THINGS WERE GETTING TIGHT WITH RESPECT TO OUR XING TFC; SO WE BEGAN A CLB AND STARTED A L TURN. I KEYED THE RADIO AND TOLD THE CTLR WE WERE CLBING AND TURNING THAT HE WAS GIVING INSTRUCTION TO THE WRONG ACFT BUT WE WERE COMPLYING. BY NOW THE POOR GUY WAS A BASKET CASE. BOTH OF US WERE CLBING AND TURNING EVEN THOUGH HE NEVER SPECIFICALLY CALLED US BY OUR CORRECT NUMBER. AS IT TURNED OUT HE REALLY WAS TRYING TO DIRECT OUR ACFT BUT NEVER GOT OUR CALL SIGN CORRECT. WE SAFELY MISSED THE XING TFC AND NEVER RECEIVED A TA. WE ALSO NEVER RECEIVED CLRNC TO DO WHAT WE DID BECAUSE THE CTLR ISSUED ALL HIS INSTRUCTIONS TO OUR SISTER SHIP. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THE 2 COMPANY ACFT WERE G200'S AND THAT THE CTLR SENT THEM OFF TO NEW FREQS WITHOUT EVER ACKNOWLEDGING THAT THERE HAD BEEN A PROB.