C90 CTLR AND FLC CONFUSE CALL SIGNS AND THE FLC TAKES A CLRNC FOR ANOTHER ACFT.

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ORD APCH CTL/ATC HAS HAD TROUBLE WITH OUR CALL SIGNS. WE USE ACR X XYZ AND THEY CALL US ANYTHING FROM ACR Y TO ACR Z AND CONSTANTLY TRANSPOSE THE FLT NUMBERS. DURING THIS FLT; WE WERE THE ONLY ACR X ACFT ON APCH FREQ. WE WERE ON A BASE LEG VECTOR FOR ILS RWY 4R. 3 PREVIOUS TIMES; THE CTLR KEPT CALLING US ACR X XXYZ INSTEAD OF XZYZ. WE ALWAYS CORRECTED THE CTLR. HE GAVE US A TURN TO 070 DEGS; 4000 FT; INTERCEPT THE ILS RWY 4R; MAINTAIN 4000 FT UNTIL ESTABLISHED; CLRED FOR THE APCH. OUR POS LOOKED GOOD OFF THE ORD VOR FOR THE 070 DEGS TO WORK. MY COPLT THOUGHT APCH USED THE WRONG CALL SIGN; SO I TOLD HIM TO CONFIRM. BECAUSE WE COULD TALK TO HIM (90 SECONDS LATER) HE GAVE US A L TURN TO 010 DEGS AND SAID WE HAD TAKEN SOMEONE ELSE'S TURN. 1/2 WAY THROUGH THE TURN; HE TURNED US BACK AGAIN TO THE R TO INTERCEPT. WE ASKED FOR CLRNC LOWER AND GOT 2500 FT. THE APCH WORKED OUT OK; NO CONFLICTS WERE NOTED. I THINK THE CTLRS GET USED TO WORKING THE SAME FLT NUMBERS ON THEIR DAILY SHIFTS AND WITH OUR CALL SIGN/FLT NUMBERS BEING NEW; IT ADDS CONFUSION TO THEIR DAY. OR; WE JUST TOOK SOMEONE ELSE'S APCH CLRNC.