ACFT IDENT MIX UP AND ISSUANCE OF POS AND HOLD TO WRONG ACFT WITH SUBSEQUENT TKOF CLRNC BY TWR AT MEM; TN.

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WE WERE CLRED TO TAXI TO THE ASSIGNED ACTIVE RWY; COMPLETED OUR ASSIGNED CHKS AND CHKLISTS AND WERE NOT AWARE OF ANY IRREGULARITY IN ACFT SEQUENCING. WHEN WE WERE #1 FOR DEP; ATC CLRED A COMPANY AVRO INTO POS AND HOLD WITH A SIMILAR BUT DIFFERENT CALL SIGN; SO WE READ BACK THE POS AND HOLD CLRNC USING OUR CORRECT FLT NUMBER; HEARD NO ATC QUESTIONS TO; OR OTHER VERIFICATIONS OF THE DIFFERENCE AND PROCEEDED INTO POS AND HOLD. WE THOUGHT THAT BY OUR READING OUR NUMBER BACK TO THEM AND THEIR NO DIRECT RESPONSE OR QUESTIONING OF IT THAT IT WAS JUST A STRIP OUT OF ORDER AND THEY HAD CORRECTED IT. WHAT WE SHOULD HAVE DONE IS NOT HAVE ENTERED THE RWY WITHOUT VERBAL CONFIRMATION OR ACKNOWLEDGEMENT OF THE DIFFERENCE. WE REALIZED THAT ATC HAD NOT CORRECTED OR RECEIVED OUR DIFFERENT FLT NUMBER WHEN A SHORT TIME LATER THEY CLRED THE PREVIOUSLY ISSUED FLT NUMBER FOR TKOF AND OUR FLT NUMBER INTO POS AND HOLD. AT THIS TIME WE CLARIFIED WHO WE WERE; RECEIVED CLRNC FOR TKOF AND LEFT WITHOUT ANY CONFLICTS OR NEAR MISS EVER INVOLVED. HOW WE GOT OUT OF SEQUENCE IS HARD TO UNDERSTAND. I BELIEVE THE MIX-UP PROBABLY HAPPENED IN THE SEQUENCING OF STRIPS IN THE TWR (I KNOW I AM BLAMING THE OTHER GUY) BECAUSE OUR COMPANY ACFT COME OUT OF THE SAME AREA; AND IN GOING TO THE ACTIVE RWY; UNLESS YOU PULL OFF FOR A PROB OR NUMBERS; IT IS NEAR IMPOSSIBLE TO CHANGE YOUR SEQUENCE ONCE STARTED OUT TO THIS RWY. THAT SAID THOUGH; WE SHOULD HAVE NEVER WENT INTO POS AND HOLD WITHOUT CLARIFYING AND CORRECTING WHAT WAS A BLATANT DISCREPANCY IN FLT NUMBERS. WE TOO WERE AT FAULT.