G2 DEP FROM VNY EXPERIENCED CONFUSION WITH ZLA CTLR REGARDING SIMILAR ACFT NUMBER AND ROUTING.

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WE DEPARTED VNY. OUR FLT PLAN WAS TO FLY OVER LAS VEGAS; NM. THIS RTE WAS SELECTED TO TAKE ADVANTAGE OF FAVORABLE WINDS. AS WE WERE CLBING OUT AND HANDED OVER TO LA; WE WERE GETTING VECTORED L OFF COURSE. UNBEKNOWNST TO US; THERE WAS ANOTHER ACFT WITH A SIMILAR CALL SIGN ON FREQ. THE OTHER ACFT ACKNOWLEDGED A RADIO XMISSION THAT I NOW REALIZE WAS FOR US WHICH WAS 'CLRED DIRECT LAS VEGAS; NV.' WHILE THE OTHER ACFT IS TURNING THE WRONG WAY I'M STILL EXPECTING A R TURN DIRECT LAS VEGAS. EVENTUALLY THE CTLR ASKED US WHAT WE WERE DOING WHICH WAS 'STILL ON A VECTOR' WHICH HE SAID GO DIRECT LAS VEGAS AND WE TURNED DIRECT LAS VEGAS. (I BELIEVE THE CTLR PHONETICALLY SPELLED LAS AND WE ENTERED LVS NOT KNOWING AND NOT ADVISED THAT OUR CLRNC HAD CHANGED.) ONCE THE CTLR SAW WE WERE NOT GOING WHERE HE THOUGHT; WE GOT A VECTOR TO THE L TOWARD LAS AND QUERIED THE CTLR ABOUT OUR ROUTING. IT WAS NOW THAT HE SAID WE WERE GOING TO LAS AND NOT LVS. SO NOW WE ARE ON A VECTOR AND AS WE ARE ABOUT TO ROLL OUT 020 DEGS DIRECT LAS; THE CTLR ASKS US TO TURN 40 DEGS R WHICH WE DID. AS HE SEES US TURNING R; HE MAKES THE STATEMENT; 'THAT 40 DEG TURN WAS FOR THE OTHER ACFT.' OBVIOUSLY IF I DIDN'T THINK IT WAS FOR US I WOULD NOT HAVE ACKNOWLEDGED IT. NOW THE CTLR IS IN TROUBLE -- I'M NOT GOING WHERE HE THINKS I AM AND THE OTHER ACFT IS ALSO HEADING IN THE WRONG DIRECTION. AND WITH LA ARRS OVERHEAD AND RESTR AREAS EVERYWHERE AND MAX NUMBER OF ACFT TO CTL -- THERE IS CHAOS. ONCE EVERYTHING IS SORTED OUT HE ASKED ME TO CALL HIS SUPVR; WHICH I DID. THE SUPVR SAID THERE WERE NO VIOLATIONS BUT WE SHOULD 'LISTEN UP.' I FEEL WE WERE. THERE WAS A LOT OF CONFUSION WITH THE SIMILAR CALL SIGNS; LAS VEGAS; NV; AND LAS VEGAS; NM; AND NOT BEING ADVISED OF MY RERTE IN A 'STANDARD' MANNER.