AN AIR CARRIER FLIGHT CREW ACCEPTED A GROUND TAXI CLEARANCE FOR A COMPANY AIRCRAFT WITH A SIMILAR SOUNDING CALL SIGN. SUBSEQUENT CONTROLLERS THEN ATTEMPTED TO CONTROL THE FLIGHT TO AN INCORRECT DESTINATION.

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I WAS OPERATING ACFT X DEPARTING ZZZ. DEP TIME WAS APPROX XA25 AM LCL TIME. AT THE GATE; I LISTENED TO ATIS AND CALLED CLRNC DELIVERY FOR OUR CLRNC. TO THE BEST OF MY KNOWLEDGE I USED OUR CORRECT CALL SIGN; 'ACFT X.' AFTER REVIEWING OUR CLRNC BOTH THE CAPT AND MYSELF VERIFIED THE CORRECT XPONDER CODE INPUT. WHEN IT WAS TIME TO PUSH BACK I CALLED RAMP; AGAIN TO THE BEST OF MY KNOWLEDGE; USING OUR CORRECT CALL SIGN. ONCE PUSHED BACK AND THE ENGS STARTED; I ASKED RAMP TO TAXI. RAMP CLRED US TO TAXI TO TXWY 'P' WHERE WE THEN CALL GND FOR FURTHER TAXI INSTRUCTIONS. ONCE NEAR POINT PAPA; I THEN CALLED GND IDENTING US AS; 'ACFT X POINT PAPA READY TO TAXI.' WE WERE TOLD TO 'TAXI TO XXR VIA CHARLIE AND ROMEO BEHIND THE 757' OFF OUR NOSE. I READ BACK THE CLRNC AND WE PROCEEDED TO XXR. ONCE NEAR XXR WE SWITCHED FREQS TO MONITOR TWR. WE WERE THE ONLY COMPANY ACFT WAITING FOR TKOF; UNLESS ONE WAS BEHIND US THAT WE COULD NOT SEE. ONCE OUR TURN CAME WE WERE CLRED FOR TKOF BEHIND ANOTHER ACR AIRBUS. TO THE BEST OF MY KNOWLEDGE I READ BACK THE APPROPRIATE CALL SIGN; 'ACFT X CLRED FOR TKOF.' THE CAPT TAXIED ONTO RWY XXR AND XFERRED THE CTLS TO ME. EVERYTHING UP TO THIS POINT WAS UNEVENTFUL. WE WERE HANDED OVER TO DEP BY THE TWR AROUND 1000 FT AGL. THE CAPT CALLED DEP TO CHK IN. FROM THIS POINT ON THERE WAS CONFUSION ON OUR CALL SIGN. I BELIEVE THE CAPT USED OUR CORRECT FLT NUMBER AND THE DEP CTLR ASKED US TO IDENT. WE DID SO AND THE DEP CTLR ASKED ABOUT OUR SQUAWK AS WELL AS GAVE US A NEW ONE. WE THEN CHANGED OUR SQUAWK PER HIS REQUEST. THERE MAY HAVE BEEN CONFUSION WITH ANOTHER ACR FLT Y IN THE VICINITY. DEP ASSIGNED US A HIGHER ALT THAN WE NORMALLY FLY TO ZZZ2 FROM ZZZ1 AND WE QUESTIONED IT REQUESTING A LOWER ALT; 17000 FT VERSUS FL210. WE CONTINUED FLYING THE SID LEVELING OFF AT 7000 FT MSL FOR TFC. AT SOME POINT DURING ALL OF THIS I BELIEVE ATC ISSUED OUR ORIGINAL SQUAWK BACK AND THE CAPT CHANGED THE XPONDER TO REFLECT THAT. WE WERE HANDED TO THE NEXT CTLING AGENCY AND ADVISED TO CALL ZZZ1 APCH ONCE ON THE GND AT ZZZ2. SUPPLEMENTAL INFO FROM ACN 804686: I WAS WORKING GND; ACFT X CALLED FOR TAXI WHILE I WAS CORRECTING ANOTHER ACFT OF A BAD READBACK OF THE RWY ASSIGNMENT. I THEN ISSUED A CLRNC TO ACFT Y TO TAXI TO RWY XXR. I THOUGHT I HEARD ACFT Y READ BACK THE INSTRUCTIONS. ACFT X ACCEPTED THE CLRNC FOR ACFT Y. ACFT X THEN ACCEPTED MULTIPLE CLRNCS FOR ACFT Y AND GOT AIRBORNE AND CAUSED A DEV.