ACR MLG UNAUTH TKOF FROM SJC IN RESPONSE TO WRONG CALL SIGN.

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TAXIING OUT WE WERE SEQUENCED BEHIND AN ACR Y MLG. THERE WAS SOME CONFUSION ON GND CTL AND THE ACR Y WAS MISIDENTED AS AN ACR Z. AT ONE POINT A SUPVR HAD TO COME ON THE FREQ TO MAKE THE RIGHT IDENT. AS WE APCHED THE END OF THE RWY WE WERE TOLD TO GO TO TWR FREQ 120.7. THIS WAS UNUSUAL; SINCE THIS IS THE FREQ FOR THE SHORT RWY THAT THE GA PLANES USE. THE TWR WAS USING 1 FREQ FOR BOTH RWYS AND THE TWR OPERATOR WAS OVERLOADED; AS WELL AS THE FREQ. WE WERE #1 FOR TKOF AT THE END OF THE RWY; RWY 30L. THERE WAS NO ONE IN FRONT OF US SINCE ACR Y HAD BEEN CLRED FOR TKOF. WE COULD HEAR THE TWR CALLING OUT THE NUMBER OF ANOTHER ACFT; CLRING THEM FOR IMMEDIATE TKOF. THE TWR CALLED THE # AT LEAST 2 TIMES POSSIBLY 3; CALLING FOR IMMEDIATE TKOF. SINCE WE WERE #1 AND THERE WAS NO OTHER ACFT IN SIGHT AND THERE ALREADY HAD BEEN CONFUSION WITH CALL SIGNS AND NO ONE IN FRONT OF US; I ASKED THE F/O TO ASK IF THEY WERE CALLING US AND DID THEY MEAN THAT WE WERE CLRED FOR TKOF. AT THIS POINT THE TWR OPERATOR APPARENTLY THOUGHT THE OTHER ACFT HAD CALLED AND SAID 'YES; CLRED FOR TKOF.' I TOOK THE RWY AND AS I LINED UP ROLLING TOWARDS THE CENTERLINE I LOOKED UP THE FIELD AND NOTED THAT THERE WAS ANOTHER COMPANY ACFT AT THE INTXN HOLDING SHORT OF THE RWY. HE WAS THE OTHER NUMBER THAT THEY HAD BEEN CALLING; BUT HAD JUST COME OVER TO THE FREQ. I INSTRUCTED THE F/O TO VERIFY THAT WE WERE THE ONE CLRED FOR TKOF. THE TWR RESPONDED BY CANCELLING THE OTHER ACFT'S TKOF CLRNC AND ONCE AGAIN CLRED US TO GO. INITIALLY WE WERE CALLED BDEF AND THEN CORRECTLY BCEF. I HAVE BEEN FLYING OUT OF SJC SINCE THAT EARLY 1960'S; I HAVE NEVER SEEN AN ACR TKOF FROM THAT INTXN. WE WERE NEVER INFORMED OF HIM OR MADE AWARE THAT THERE WOULD BE SOMEONE ELSE DEPARTING AHEAD OF US. THE ENTIRE PROB COULD HAVE BEEN AVOIDED; I BELIEVE; BY USING DIFFERENT FREQS OR AT LEAST INFORMING US THERE WOULD BE A DOWNFIELD DEP.