A PIC OF A B757 ANSWERS FOR THE WRONG CALL SIGN WHILE THE FO IS ON THE PA AND PERFORMS AN UNAUTH TKOF FROM DTW; MI.

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WE WERE CLRED TO TAXI TO RWY 21C BEHIND A B737. AFTER HIS DEP; WE WERE TOLD TO HOLD SHORT AND EXPECT A 5-7 MIN CTR DELAY. FO STARTED TO MAKE A PA TO ADVISE PAX AND THEN WE WERE TOLD TO 'TURN L TO 200 DEGS; CLRED FOR TKOF.' AFTER PASSING 2500 FT WE WERE TOLD TO STOP OUR CLB AT 3000 FT. THERE WAS A DC9 THAT DEPARTED RWY 21R THAT WE WERE WATCHING. THEY GAVE HIM A L TURN IN FRONT OF US THEN CONTINUED OUR CLB. WHEN ON CTR FREQ THEY ASKED US TO CALL DTW TWR WHEN WE WERE ON THE GND. THE TWR OPS SUPVR TOLD ME HE REPLAYED THE TAPES AND HEARD US ACKNOWLEDGE THE CLRNC TO TURN L TO 200 DEGS AND CLRED FOR TKOF WITH OUR CALL SIGN. HE SAID THE CTLR FAILED TO RESPOND TO OUR ACKNOWLEDGEMENT BUT THE TKOF CLRNC WAS FOR AN ACFT WITH A SIMILAR CALL SIGN ON RWY 21R. THE CTLR WAS WORKING MORE THAN 1 FREQ. HE SAID THERE WAS NO CONFLICT WITH TFC. SUPPLEMENTAL INFO FROM ACN 466598: I SELECTED THE PA SYS ON MY COM PANEL TO INFORM THE PAX OF OUR SIT. OVER THE CAPT'S SPEAKER; I HEARD A TKOF CLRNC GIVEN. THE CAPT RESPONDED; REPEATED THAT WE WERE CLRED FOR TKOF; WITH A TURN TO A 200 DEG HDG. AFTER WE WERE AIRBORNE; TWR DIRECTED TFC OFF RWY 21R THAT DEPARTED AHEAD OF US TO TURN AND MAINTAIN 5000 FT. WE WERE DIRECTED TO MAINTAIN 3000 FT. THIS SIT RE-EMPHASIZES THE NEED FOR CLR COM BTWN PLTS AND ATC. AT LEAST 3 ACTIONS COULD HAVE PREVENTED THE OCCURRENCE. 1) THE CAPT; WHO ANSWERED TWR'S TKOF CLRNC CALL; MUST BE ABSOLUTELY CERTAIN OF THE CALL SIGN THE CLRNC WAS GIVEN TO. 2) THE FO MUST QUESTION ANY ACTION OR CLRNC THAT IS QUESTIONABLE; IE; ONE MIN WE WERE NOTIFIED OF A 5 MIN DELAY; AND THE NEXT MIN WE WERE CLRED FOR TKOF. 3) ATC MUST LISTEN TO THE RESPONSE(S) OF HIS CLRNCS AND BE READY TO CORRECT ANY MISTAKES.