AN ACR ACFT REJECTED ITS TKOF WHEN SFO TOWER CALLED 'CANCEL THE TKOF CLRNC.' TWO ACFT WITH IDENTICAL NUMBERS WERE ON ADJACENT RWYS. BOTH REJECTED.

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SFO TWR CLRED US (FLT XYZ) FOR TKOF ON RWY 1R. PUSHED THE PWR TO TOGA. AS I AM CHKING THE INSTS AND ACCELERATING; WE HEARD THE NUMBER 'XYZ CANCEL TKOF CLRNC;' FO QUICKLY SAID CANCEL TKOF; AT WHICH TIME I WAS BRINGING THE PWR PACK TO INITIATE THE 'ABORT/REJECTED TKOF.' WE REJECTED AT AROUND 65 KTS SO WE NEVER HAD THE BRAKES ACTIVATED AND IT WAS A GRADUAL STOP. THERE WAS ANOTHER ACR JET APPROX 2 MI ON FINAL. CLRNC HAD BEEN ISSUED TO 'ACR FLT XYZ ON THE ADJACENT RWY 1L.' ACR Y HAD TAKEN TOO MUCH TIME TO ROLL SO HIS TKOF CLRNC WAS REVOKED. THERE WAS NEVER ANY TFC CONFLICT WITH ANYTHING. ACR Y WAS TOLD TO GAR SINCE TWR THOUGHT I WOULD NOT BE STOPPED BY THE INTXN OF RWY 28L; BUT WE EXITED ON TXWY F TO THE R AND RETURNED TO OUR TKOF POINT. I MADE AN ANNOUNCEMENT; PAX WERE INFORMED OF THE EVENT AND I REASSURED THEM IT WAS BEST TO CANCEL THE TKOF AND THE REASON WHY WE DID IT. NO FURTHER ISSUES ENSUED. SIMILAR NUMBERS HAS BEEN A DETRIMENT AND A SAFETY ISSUE FOR MANY YRS. NEVERTHELESS; THE ISSUE HERE WAS SIMILAR NUMBERS DURING A CRITICAL PHASE OF FLT.