ACR LGT TRACK HDG DEV ON VECTOR DEP FROM LAX.

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CLRED FOR TKOF; FLY 235 DEGS; MAINTAIN 5000 FT. PASSING ABOUT 1000 FT THE TCASII BEGAN TO SOUND 'TFC; TFC' AS IT OCCASIONALLY DOES AT THAT POINT. I TOOK A FREQ CHANGE TO DEP AT THIS TIME AND RPTED. THE FIRST WORDS I HEARD WERE 'DO YOU STILL HAVE COMMUTER IN SIGHT'? I REPLIED; 'NEGATIVE; BUT I HAVE THE LARGE ACFT AT 12 O'CLOCK'. 10 SECONDS LATER I GOT A SECOND TCASII WARNING AND INSTRUCTIONS TO TURN TO 160 DEGS AND CLB TO 13000 FT. THIS SEEMED EARLY BUT BECAUSE OF THE SECOND (UNUSUAL) TCASII WARNING; THE COMMUTER RPT AND POSSIBLE COAST TFC; REASONABLE. I REPEATED THE HDG AND ALT AND BEGAN TO TURN; CONTINUING MY CLB. DURING THE TURN; PASSING ABOUT 4000 FT DEP ADVISED ME TO STOP TURN AND MAINTAIN 5000 FT; WHICH I DID. I RPTED AN LGT IN SIGHT TO MY R AND WELL ABOVE ME. HE HAD TAKEN OFF IN FRONT OF ME AND MADE HIS CLBING L TURN TOWARDS LAX. IT WAS TENSE AT THIS TIME. VISIBILITY WAS GOOD; BUT I WAS STILL CONCERNED ABOUT THE COMMUTER CALL AND POSSIBLE COAST TFC. DEP LATER ADVISED ME THAT I HAD TAKEN ANOTHER ACFT'S TURN; COMPANY CCB. I MADE A TCASII SYS LOGBOOK WRITEUP SINCE I WAS UNABLE TO DETERMINE THE VALIDITY OF THE WARNING. THERE WERE NO RA'S; ONLY TA'S. THE SYS CHKED OK. THE SIMILARITY OF CALL SIGNS HAS BEEN BROUGHT TO THE ATTN OF THE COMPANY. A TCASII EVENT QUESTIONNAIRE HAS BEEN COMPLETED SUGGESTING THAT TCASII VOLUME BE INHIBITED FOR THE FIRST 90 SECONDS AFTER TKOF.