CTLR VECTORS WRONG ACFT AFTER DEP AND CONFLICTS WITH AN ARR ACR RESULTING IN LTSS.

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THE INCIDENT OF A NEAR MISS OR OPERATIONAL ERROR OCCURRED ON THE DATES AND TIMES ABOVE WERE CAUSED WHILE I WAS WORKING THE TWR POS AT O'HARE TWR. DURING A PERIOD OF MODERATE TFC (DEPARTING 9L AND 32L) I MISTAKENLY GAVE A HDG TO THE INCORRECT COMPANY AIRLINES FLT. BY GIVING CTL INSTRUCTIONS TO THE INCORRECT FLT; I CAUSED A FLT (ACR X) TO PASS OVER AN ACFT ON THE 9R FINAL APCH COURSE. THE PROBLEM WAS DISCOVERED WHEN THE PLT QUESTIONED THE ASSIGNED HDG. I QUICKLY TOOK EVASIVE ACTION AND TURNED ACR X FROM FURTHER CONFLICTS. WHAT CONTRIBUTED TO THE INCORRECT CALL SIGN WAS A RPT FROM ANOTHER CTLR OF A MISSED APCH HDG FOR MY AIRSPACE. I WAS IN THE PROCESS OF SENDING ACR X TO DEP CTL WHEN THE OTHER CTLR YELLED IN THE CAB 'GOING AROUND 4 R.' IN THE MIDST OF MY XMISSION TO SHIP ACR X TO DEP; I INSTEAD TURNED HIM TO A HDG 090 (HE WAS ALREADY ON A 330) THINKING HE WAS THE COMPANY FLT ALSO AIRBORNE OFF OF 9L. (THE ONE I REALLY NEEDED TO TALK TO ABOUT THE MISS APCH). TO PREVENT A RECURRENCE I WOULD SUGGEST THAT TO MYSELF I PAUSE TO CONSIDER THE MISSED APCH AND NOT REACT TOO QUICKLY ESPECIALLY IF NOT NECESSARY. ALSO POSSIBLY MORE STANDARDIZATION OF MISSED APCHS AT O'HARE.