A CANADAIR REGIONAL JET FLC RECEIVED A TCASII TA AFTER ACCEPTING A CLB CLRNC INTENDED FOR ANOTHER ACFT.

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WE WERE LEVEL AT FL270. ZOB ISSUED A CLB TO FL290 FOR APPARENTLY IT WAS FOR ACFT Y. I READ BACK THE NEWLY ASSIGNED ALT FOLLOWED BY OUR CALL SIGN; 'ACFT X.' THEN I INITIATED A 500 FPM CLB TO FL290. IMMEDIATELY WE RECEIVED A TCASII TA. WITHIN SECONDS; I LOCATED THE TFC ON TCASII AND VISUALLY. I DISCONNECTED THE AUTOPLT AND LEVELED OFF AT 27200 FT WHILE TRYING TO CONTACT ZOB. THE TFC PASSED UNEVENTFULLY AT FL280. AFTER THE 3RD CALL; ATC RESPONDED; TELLING US TO MAINTAIN FL270 AND ACFT Y TO MAINTAIN FL290. THE CTLR THEN ASKED US IF WE HAD TAKEN ANOTHER ACFT'S ALT ASSIGNMENT; AND I TOLD THE CTLR THAT WE READ BACK 'FL290; ACFT X.' HE AGAIN STATED THAT THE CALL WAS FOR ACFT Y. HE ALSO STATED THAT WHEN DOING THIS FLT IN THE FUTURE; WE SHOULD BE VERY CAUTIOUS OF THE COMPANY ACFT'S SIMILAR CALL SIGN. THESE CALL SIGNS WERE VERY DIFFICULT TO DIFFERENTIATE. POSSIBLY; IF THE CTLR HAD REALLY EMPHASIZED THE 1ST NUMBER IN THE CALL SIGNS; THIS SIT COULD HAVE BEEN AVOIDED. IT IS VERY IMPORTANT FOR CREWS TO BE VIGILANT IN LISTENING TO CALLS FROM ATC; HOWEVER IT IS JUST AS IMPORTANT FOR ATC TO LISTEN FOR CORRECT READBACKS. THANKS TO TCASII ON THIS ONE. SUPPLEMENTAL INFO FROM ACN 447972: I WAS GIVING AN ANNOUNCEMENT TO PAX AND CTR GAVE US A CLB FROM FL280 TO FL290. CAPT READ BACK INSTRUCTION AND JUST STARTED THE CLB.