AN ACR MLG TAXIED OUT USING ONE CALL SIGN; BUT TWR KEPT CALLING HIM ANOTHER CALL SIGN. WHEN AT THE RWY TWR CLRED THE MLG FOR TKOF WITH THE OTHER CALL SIGN AND THE ACFT TOOK OFF. ONCE AIRBORNE AND ON DEP CTL FREQ THEY WERE TOLD THAT DEP CTL DID NOT HAVE A FLT PLAN FOR THE CALL SIGN THE ACFT WAS USING. UPON LNDG THE RPTR CALLED LAX TWR; AND WAS TOLD THE FLT PLAN FOR THE CALL SIGN THE ACFT USED WAS NOT IN THE SYS; YET THE RPTR SAID HE HAD A PDC FOR IT.

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FLT XABC DEPARTING FROM GATE RECEIVED TAXI CLRNC TO RWY 25R LAX. SWITCH TO TWR FREQ WHEN HOLDING SHORT OF RWY. TWR PROCEEDED TO CLR US INTO POS AND HOLD BY USING CALL SIGN XADC. WE RESPONDED WITH POS TO HOLD ACR XABC (WITH EMPHASIS ON XABC). WE WERE THEN CLRED TO TKOF AS FLT XADC. WE RESPONDED AGAIN AS FLT XABC CLRED FOR TKOF. NO RESPONSE BACK BY TWR; SO WE SUSPECTED OCCASIONAL MIXUP WITH NUMEROUS SHUTTLE CALL SIGNS (ALL XXXX #'S). AFTER CHKING IN WITH DEP AS XABC WE WERE INFORMED THAT THEY DID NOT HAVE A FLT PLAN ON US. WE TOLD THEM OUR ROUTING AND WE PROCEEDED TO PDX AS FILED! UPON ARRIVING IN PDX CALLED LAX TWR AND TALKED WITH SUPVR. HE SUSPECTED WE TOOK OFF WITHOUT AN ACTIVE FLT PLAN. HOWEVER; WE HAD OUR PDC AS XABC WITH SQUAWK AND ROUTING AND WE ALWAYS RESPONDED AS FLT XABC. APPARENTLY OUR FLT PLAN DROPPED OUT OF THE ATC SYS AFTER WE PICKED UP OUR PDC; BUT PREVIOUS TO TKOF; SO WE ASSUMED WE WERE OPERATING ON OUR FLT PLAN. TWR NEVER QUESTIONED OUR RESPONSE AS XABC TO HIS CLRNC FOR XADC. WE SUSPECTED JUST A FLT NUMBER MISTAKE RATHER THAN TWR THINKING WE WERE ANOTHER FLT. BOTH TWR AND US SHOULD HAVE RECONFIRMED FLT NUMBER THAT WAS CLRED TO TKOF.