ATCT LCL CTLR USED THE WRONG CALL SIGN TO CLR AN ACR LTT FOR TKOF ON RWY 16L. THE FLC CORRECTED THE TWR CTLR AND WAS CLRED FOR TKOF WITH THE CORRECT CALL SIGN.

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WE WERE HOLDING SHORT OF RWY 16L (MONITORING TWR FREQ) AS WE WATCHED AN ACFT ON SHORT FINAL LNDG. AS SOON AS THE ACFT PASSED US; THE TWR XMITTED 'XADD; POS AND HOLD RWY 16L.' MY FO (PNF) RESPONDED WITH 'XADD; POS AND HOLD RWY 16L.' WHILE WE WAITED IN POS FOR THE ACFT TO CLR THE RWY; THE TWR ALSO CROSSED ANOTHER ACFT THAT HAD LANDED ON RWY 16R. AFTER ALL THE TFC WAS CLR THE TWR SAID; 'XAZX CLRED FOR TKOF RWY 16L; LEAVING 1000 FT TURN L HDG 130 DEGS.' AT WHICH TIME MY FO XMITTED; 'THIS IS XADD IN POS AND HOLD AT RWY 16L.' THE TWR THEN RESTATED HIS PREVIOUS CLRNC WITH THE XADD CALL SIGN. THE CTLR QUERIED US AS WE DEPARTED AND STATED HE THOUGHT HE WAS CORRECT. WE SAID WE THOUGHT WE WERE CORRECT AND DIDN'T ACCEPT OUR COMPANY'S (ACFT) CALL SIGN. WHILE IN POS AND HOLD; WE SAW OUR COMPANY COMING UP THE TXWY; OTHERWISE WE WERE THE ONLY ACFT WAITING FOR DEP. AT THE TIME OF THIS INCIDENT; THE TWR CAB WAS REDUCING THE NUMBER OF CTLRS (IE; THEY USE 1 CTLR FOR MULTIPLE POS/FREQS). WE BELIEVE THE LCL CTLR WAS WORKING THAT POS AS WELL AS GND CTL; AND CONFUSED OUR CALL SIGNS AND GEOGRAPHIC POS.