WRONG ACFT ON WRONG HDG; TCASII RESOLVES A CONFLICT.

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BEING VECTORED FOR ILS 2L BNA; ASSIGNED 070 DEG HDG TO INTERCEPT LOC. ON THIS HDG; SAW AN MLG XING OUR PATH L TO R ON A VECTOR TO 2R. BOTH OF US DECLARED THAT IT WAS ODD AN ACFT WAS BEING VECTORED IN FRONT OF US. WE WERE ABOUT TO CALL ATC ABOUT THE PROX OF ACFT WHEN WE GOT A TCASII ADVISORY 'CLB; CLB; NOW.' SIMULTANEOUSLY; ATC TOLD US TO TURN R IMMEDIATELY. WE DECLINED AS THAT WOULD HAVE PUT US ON A HDG TO THE TFC. WE TURNED ABRUPTLY L AND ATC BEGAN NEW VECTORS TO CIRCLE AROUND FOR 2L. AT THAT TIME ATC BEGAN CALLING US SPECIFICALLY BY FLT NUMBER AND ANOTHER AIRLINE BY THE SAME FLT NUMBER. I HAD ADVISED ATC THAT HIS VECTOR HAD PUT US INTO TFC BUT HE RESPONDED THAT IT WAS FOR ANOTHER FLT. I CALLED THE SUPVR AND FLOOR MGR AFTER LNDG. THE FLOOR MGR ADMITTED THE CTLR'S ERROR WAS DUE TO SIMILAR CALL SIGNS AND THAT SIMILAR PROBLEMS HAD OCCURRED RECENTLY. CTLRS SHOULD ALLOW EACH FLT TO RESPOND TO A CLRNC. OFTEN; A CTLR WILL SAY THE FLT NUMBER BUT A DIFFERENT AIRLINE. IF WE HAD A CHANCE TO RESPOND BECAUSE OF THE WRONG AIRLINE NAME; THIS TYPE OF CONFLICT COULD BE AVOIDED. BUT IT WAS GOOD AND POSITIVE THAT I COULD CALL THE ATC PERSONNEL AND DISCUSS THE MATTER. IN THIS MANNER PUNITIVE ACTION CAN BE AVOIDED. IT IS A POSITIVE RESULT INSTEAD OF NEGATIVE.