ACR-LGT ANSWERED CLRNC FOR ANOTHER FLT WITH SIMILAR A/N CALL SIGN CAUSING POTENTIAL CONFLICT WITH CROSSING ACR-LGT.

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ORD TWR CLRED US FOR TKOF ON RWY 32L FROM THE T1 INTXN; ASKED US TO KEEP THE PRECEDING IN SIGHT; HE WAS GOING STRAIGHT OUT AND TO TURN ASAP TO 360 DEGS. WE TOOK OFF AS CLRED; TURNED AND WAS TOLD TO CONTACT DEP. WE RPTED TO DEP THAT WE WERE LEAVING 2200' AND ON A HDG OF 360 DEGS. DEP THEN ONLY USED A NUMBER TO IDENT THE ACFT AND WE (ALL 3 OF US) HEARD OUR NUMBER; A CLRNC TO TURN LEFT TO 270 DEGS. I READ BACK THE CLRNC OF A 270 DEG HDG AND OUR NUMBER. DEP THEN GAVE US A CALL SAYING RADAR CONTACT AND CLB TO 6000'. I READ BACK THE 6000' AND ASKED ABOUT TFC AT 12 O'CLOCK AND HIGHER THAN US. THIS TFC I HAD IN SIGHT SINCE WE LEFT APPROX 2000'. WE PASSED APPROX 2500' HORIZ TO LGT C WHEN HE WAS DSNDING AND WE WERE CLBING. WE BOTH TURNED AWAY FROM EACH OTHER TO INCREASE SEP. WE ALSO HAD THE MDT X IN SIGHT AT ALL TIMES AND DUE TO OUR CLB DURING THE INCIDENT; I BELIEVE THAT THE 270 DEG TURN WAS ISSUED TO ANOTHER ACFT. WHEN I CALLED BACK WITH MY ACKNOWLEDGEMENT OF ACR ICG; 'TURN LEFT TO 270;' THAT CONFIRMED IT. THERE WAS ALSO AN ACR B IVG ON THE FREQ. IF CTLRS WOULD LISTEN TO THE READBACK; OR THE SQUEAL IN THE CASE OF 2 AIRPLANES ANSWERING; AND USE COMPANY NAMES IN THEIR CALLS; THIS WOULD NOT HAPPEN. SUPPLEMENTAL INFO FROM ACN 95272: THE CONFLICT WAS BTWN LGT ICG AND ANOTHER COMPANY LGT C ON LEFT DOWNWIND FOR RWY 9R AT ORD. LGT ICG HAD CONTACT WITH THE OTHER LGT C AT ALL TIMES. DEP CTL ASKED IF WE SAW THE OTHER LGT C. WE SAID WE DID. SHE SAID NO PROB AND SWITCHED US TO CENTER FREQ.