AN ACR LGT; CALL SIGN ABC; WAS GIVEN INSTRUCTIONS FOR ANOTHER ACFT OF THE SAME ACR; CALL SIGN ACB.

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WE WERE FLYING ACR X FLT ABC. JUST OUTSIDE THE FAF ON THE ILS TO RWY 35L; THE FINAL APCH CTLR ISSUED US A HDG OF 180 DEGS AND A LEVELOFF OF 7500 FT. SINCE THIS WAS ABOUT A 180 DEG TURN; WE ASKED THE CTLR TO CONFIRM THE INSTRUCTIONS AND HE REPEATED THEM. WE THEN ASKED WHICH DIRECTION TO TURN AND WERE TOLD TO TURN R. WE INITIATED THE MANEUVER AND ASKED THE REASON SINCE WE WERE NOW TURNING TOWARD TFC ON THE RWY 35R APCH. WE WERE TOLD THAT THERE WAS A FLT WITH A SIMILAR CALL SIGN (ACR X FLT ACB) AND THAT THE CTLR HAD INTENDED TO GIVE THAT ACFT THE TURN. 3 RADIO CALLS HAD BEEN GIVEN TO US WITH OUR CORRECT CALL SIGN; AND ALL HAD BEEN ACKNOWLEDGED BY US USING OUR CALL SIGN. ALTHOUGH THERE WAS TFC ON TCASII; NO TA'S OR RA'S WERE TRIGGERED. GREATER CARE SHOULD BE TAKEN TO EITHER AVOID (FLT NUMBER SCHEDULING?) OR BE MADE AWARE OF POSSIBLE CONFLICTS IN CALL SIGNS. IF WE HAD KNOWN BEFORE THE FACT THAT A FLT WITH A SIMILAR SOUNDING CALL SIGN WAS ON THE FREQ; WE POSSIBLY COULD HAVE CLRED UP THE MATTER WITHOUT HAVING TO DISCONTINUE THE ILS APCH.