ACR A LGT WITH SAME CALL SIGN AS ACR B CROSSED RWY ON CLRNC FOR ACR B.

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ON GND FREQ 121.75 WE WERE GIVEN CLRNC TO TAKE THE OUTER TO THE STUB TO THE RWY 9R PARALLEL TO FOLLOW A WDB. WHEN THE WDB GETS TO THE RWY 32L PARALLEL AND TURNS RIGHT WE ARE TO TURN LEFT; HOLD SHORT OF RWY 9R AND SWITCH TO TWR 120.75. WE HEARD 'XYZ CROSS 9R W/O DELAY AND GO TO POINT 9 ON THE OTHER SIDE.' THE CLRNC TO CROSS WAS ACKNOWLEDGED BY THE F/O BY USING THE FULL CALL SIGN OF ACR A XYZ. WE WERE STILL PARKED ON THE RWY 9R PARALLEL PRIOR TO THE CORNER AND IT TOOK AT LEAST 30 SECS OR MORE TO REACH THE RWY. TWR DID NOT QUESTION OUR ACKNOWLEDGEMENT. THE RWYS IN USE FOR LNDG WERE RWY 4R AND RWY 9R. AFTER XING RWY 9R WE WERE TOLD THAT WE DIDN'T HAVE CLRNC TO CROSS AND THAT THE CLRNC WAS FOR ACR B XYZ. HE ALSO SAID THAT THE TWR DIDN'T HAVE A STRIP ON US. APPARENTLY ACR B XYZ LANDED ON RWY 4R AND WAS HOLDING SHORT OF RWY 9R ON THE HIGH SPEED TURNOFF AT RWY 4R. WE WERE NOT AWARE THAT THERE WAS AN ACR B XYZ UP TO THIS POINT. WE WERE THE ONLY XYZ THAT HAD BEEN ON THE FREQS; SO WHEN TWR CALLED XYZ WE ACKNOWLEDGED; USING OUR COMPLETE CALL SIGN OF ACR A XYZ. GND TOLD ACR B XYZ THAT HIS XMISSIONS HAD BEEN BLOCKED BY ANOTHER ACFT; APPARENTLY US; AND GAVE HIM INSTRUCTIONS TO TAXI TO THE GATE. SUPPLEMENTAL INFO FROM ACN 90077: WE WERE NOT AWARE THAT THERE WAS AN ACR B XYZ AS WE WERE THE ONLY XYZ ON THAT FREQ UP TO THAT TIME. SO; WHEN THE TWR CALLED; WE ACKNOWLEDGED USING OUR COMPLETE CALL SIGN OF ACR A XYB. APPARENTLY TWR WAS ALSO NOT AWARE THAT HE HAD 2 FLT NUMBER ACFT HOLDING SHORT OF THE SAME RWY. HAD HE KNOWN AND USED THE FULL ACR B XYZ ACR B; OR HAD WE BEEN WARNED THERE WERE 2 XYZ'S ON THE SAME FREQ; THE PROB COULD HAVE BEEN AVOIDED.