AN A320 CAPT ADMITTED THAT HIS FO RESPONDED TO A SIMILAR SOUNDING CALL SIGN IN D21 AIRSPACE; CAUSING HDG DEVS.

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I WAS PF WHEN WE WERE TAKING OFF ON RWY 22L AT DTW. RWY 21R WAS CLOSED; AND THERE WERE NO DEPS ON RWY 21L THAT WE WERE AWARE OF; SINCE THAT WAS THE LNDG RWY. DTW TWR GAVE US A TKOF CLRNC WITH THE INSTRUCTION I WOULD APPRECIATE A GOOD TURN TO 185. WE WERE CLBING WITH A PROMPT TURN WHEN TWR SAID THANKS FOR THE GOOD TURN AND CONTACT DEP CTL. WE SWITCHED TO DEP CTL AT 2300 FT MSL; AND I HEARD ANOTHER ACR TURN TO 050 DEGS. THE FO RESPONDED WITH OUR CALL SIGN HDG 050 DEGS. WE HAD NOT DONE THE USUAL CHK IN VERIFICATION PROC OF STATING OUR PASSING ALT AND OUR CLRED ALT. SINCE THERE WAS NO NEGATIVE RESPONSE FROM DTW DEP CTL; I ASSUMED I HAD HEARD THE OTHER CALL SIGN INCORRECTLY AND WAS TURNING TO A 050 DEG HDG WHEN I HEARD DEP CTL CALL THE OTHER ACR. I THEN REALIZED WE HAD PROBABLY TAKEN THEIR HDG BY MISTAKE. WE WERE ATTEMPTING TO CLARIFY OUR HDG WHEN DEP CTL ASKED ABOUT OUR HDG. WE TOLD HIM WE HAD TAKEN OTHER FLT'S HDG BY MISTAKE. HE TOLD US TO TURN IMMEDIATELY TO 160 DEG AND STOP OUR CLB. WE RESPONDED WITH BOTH REQUESTS IMMEDIATELY. THERE WERE NO TCASII ALERTS; AND THE CTLR DID NOT SEEM TO BE UPSET WITH OUR ERROR. WE THEN CONTINUED OUR CLBOUT WHEN INSTRUCTED TO BY DEP CTL. HE NEVER MENTIONED THE INCIDENT IN HIS XMISSIONS TO OUR FLT. UPON REFLECTION; A COUPLE OF POINTS CONTRIBUTED TO THE ERROR. WE NEVER DID THE PROPER CHK-IN PROC WITH DEP CTL. IT WAS THE LAST LEG OF A 4-DAY TRIP; AND THE FO HAD DONE A GOOD JOB UP UNTIL THAT POINT; SO I DROPPED MY GUARD A LITTLE TOO MUCH. THE REQUEST TO TURN QUICKLY TO THE INITIAL 185 DEG HDG IS A RARE REQUEST; AND MAY HAVE CONTRIBUTED TO OUR RUSHED CHK-IN PROC WITH DEP CTL. THIS NEVER WOULD HAVE HAPPENED IF THE OTHER FLT WAS NOT ON THE SAME FREQ. I SHOULD HAVE STAYED ON THE 185 DEG HDG UNTIL I VERIFIED THE CALL SIGN WITH DEP CTL. THE TURN TO A 050 DEG HDG THAT QUICKLY AFTER DEP IS A NON-STANDARD PROC. ANALYSIS: IF I WOULD HAVE TAKEN THE EXTRA FEW SECONDS TO VERIFY THE CALL SIGN; I WOULD NOT HAVE HAD TO SPEND THE COUPLE HRS WRITING THIS RPT. LESSON LEARNED.