CARJ FLC CHALLENGE CVG CTLR WHEN IT IS PERCEIVED THAT THERE IS SIMILAR COMPANY CALL SIGN CONFUSION.

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WHILE OPERATING AS FLT X; WE WERE BEING VECTORED FOR THE APCH TO RWY 36R AT CVG. IT WAS SOLID IFR CONDITIONS WITH LOW OVCST CEILINGS AND LOW VISIBILITY. AS FO; I WAS THE PF FOR THIS LEG AND THE CAPT WAS HANDLING THE RADIOS. THINGS WERE OPERATING AS STANDARD AS USUAL FOR THE CINCINNATI AREA. WE HAD RECEIVED OUR NORMAL INSTRUCTION TO SLOW OUR SPD AND FLY HDGS FOR SPACING. TO THAT POINT THE CTLR HAD NOT GOTTEN US CONFUSED WITH ANY OTHER ACFT. WE WERE HANDED OFF TO THE FINAL APCH CTLR ON 124.70. HE PROCEEDED TO GIVE US VECTORS TO INTERCEPT THE APCH COURSE FOR RWY 36R. WE WERE AT 4000 FT AND HAD JUST INTERCEPTED THE LOC WHEN HE CLRED US FOR THE ILS RWY 36R. AFTER COMMUNICATING WITH ANOTHER ACFT; THE CTLR THEN STATED 'ACR X; TURN L TO A HDG OF 090 DEGS.' I REACHED FOR THE HDG KNOB BUT STOPPED BECAUSE SOMETHING DID NOT SEEM CORRECT WITH THE INSTRUCTION. AT THE SAME TIME; MY CAPT REPLIED ON THE RADIO; 'SIR; I UNDERSTAND YOU WANT ACR X TO TURN L TO 090 DEGS?' THE CTLR STATED 'YES; ACR X; TURN L TO 090 DEGS.' MY CAPT THEN SAID; 'BUT SIR; THAT IS A 270 DEG TURN AND WILL TAKE US THROUGH THE APCH PATH FOR RWY 36L.' (RWY 36L IS THE PARALLEL RWY AND APCHS WERE BEING CONDUCTED TO THAT RWY AS WELL.) THE CTLR THEN SAID 'ACR X; YOU'RE CONFUSING ME; I NEED YOU TO FLY E.' CAPT THEN STATED 'ROGER; ACR X IS TURNING R TO E.' THE CTLR THEN SAID 'ACR X; TURN L TO HDG 030 DEGS AND INTERCEPT THE LOC TO RWY 36R.' BY THIS TIME; BOTH MY CAPT AND I WERE CONFUSED ABOUT WHAT WAS GOING ON. THE CTLR THEN ASKED US IF WE WERE ESTABLISHED ON THE RWY 36R LOC. THE CAPT THEN TOLD THE CTLR THAT 'NO; YOU JUST TURNED US OFF THE LOC TO A HDG OF 090 DEGS.' THERE WAS A SLIGHT PAUSE; AND THEN THE CTLR SAID SOMETHING LIKE 'OH NO; I KNOW WHAT HAPPENED;' AND THEN 'ACR Y; WHAT IS YOUR HDG?' THE CTLR HAD GOTTEN US (ACR X) CONFUSED WITH ACR Y WHO WAS COMING FROM THE NW AND WAS ON A DOWNWIND LEG HDG 180 DEGS. OBVIOUSLY; HAD WE NOT QUESTIONED THE CTLR'S ORIGINAL INSTRUCTIONS TO TURN L; WE COULD HAVE HAD A VERY SERIOUS ACCIDENT. WE HAD THE POSSIBILITY OF HITTING NOT ONLY THE ACFT ON THE PARALLEL APCH; BUT ALSO THE ACFT ON THE DOWNWIND; AND THE ACFT ON THE APCH BEHIND US. I DON'T PERSONALLY BLAME THE CTLR FOR THIS MISTAKE; EVER SINCE OUR COMPANY HAS GONE TO THE 4 DIGIT CALL SIGNS; CTLRS EVERYWHERE ARE GETTING THE NUMBERS MESSED UP. THERE HAVE BEEN NUMEROUS CTLRS WHO HAVE COMPLAINED ABOUT THE CALL SIGNS. I FEEL THAT UNLESS THE CALL SIGNS ARE CHANGED; THERE WILL BE A SERIOUS ACCIDENT HAPPENING. I JUST HOPE THAT IT DOESN'T TAKE THAT TO HAPPEN TO GET THIS CHANGED.