AN H25B CREW; DEPARTING SNA; WERE BROUGHT TO TASK BY ATC FOR SUPPOSEDLY NAVING ON THE WRONG VOR; PUTTING THEM IN CONFLICT WITH ANOTHER ACFT.

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HAWKER JET 800XP FLT ORIGINATED AT SNA AND DEPARTED AT APPROX XA30 FOR A GND DELAY. THE IFR CLRNC ISSUED WAS THIS: CHANNEL 1 EHF TRANSITION; MAINTAIN 10000 FT. TKOF WAS NORMAL WITH NO PROBS WITH CREW ACFT OR ATC. HDOF FROM GND TO TWR TO DEP CTL WAS ALL NORMAL. THE HDOF WAS NORMAL TO THE FIRST ZLA CTLR. WE FLEW THE PROC THROUGH OUR FMS MONITORING THE RTE AND TRANSITION WITH RAW DATA ON THE PNF (COPLT) SIDE INSTS. THE DEP WAS GOING JUST AS ISSUED WHEN WE WERE TOLD TO CONTACT ANOTHER ZLA CTLR. WE CHKED IN AND WERE TOLD RADAR CONTACT. THEN MOMENTS LATER WE WERE TOLD THAT WE SHOULD HAVE BEEN GOING TO ANOTHER VOR AND NOT LAX. THE CTLR CALLED OUT OUR CALL SIGN AND NUMBER AND I ANSWERED 'WELL OK.' I WAS SET BACK WITH THIS BECAUSE I KNEW THAT WE HAD FLOWN OVER THE VOR ON OUR DEP PROC AND THAT IT WAS 20+ MI BEHIND US ALREADY. I LOOKED OVER AT THE PF OR CAPT AND HE SHRUGGED HIS SHOULDERS AND THEN HE SAID 'I FLY; YOU FOLLOW UP WITH ATC.' I SAID OK. SO I ASKED THE CTLR IF HE KNEW THAT THE VOR HE MENTIONED WAS 20+ MI BEHIND US AND THAT WE WERE ON THIS TRANSITION THAT WAS ISSUED TO US. THE CTLR CAME BACK AND SAID THAT WE WERE IN CONFLICT WITH OTHER ACFT. THE CAPT (PF) SAID THAT THE TCASII WAS CLR AND NO CONFLICT WAS PAINTED ABOVE OR BELOW OR AT OUR ASSIGNED ALT. CAPT SHOOK HIS HEAD AND I SAID OK. WELL; AT THIS TIME WE WERE CLBING OUT OF 14500 FT TO 17000 FT THAT WAS ISSUED TO US BY THE PREVIOUS CTLR. THE CTLR DID NOT ANSWER ME. THE CTLR THEN PROCEEDED TO HAND US OFF TO ANOTHER CTLR IN A MANNER I THOUGHT INDICATED A VERY CONFUSED ATC CTLR. THE CAPT AND I TALKED ABOUT IT FOR ABOUT 1/2 HR INFLT; WE BOTH CHKED THE NOTE CARDS THAT I KEEP ON ALL ISSUED AND CHANGED CLRNCS AND CHKED THE FMS. ALL SHOWED THE COMPLETION OF THE ASSIGNED AND ISSUED DEP CLRNC. NEITHER ONE OF US WAS SURE OF WHAT HAD HAPPENED TO THE CTLR. I SAID HE MUST HAVE GOT US CONFUSED WITH ANOTHER LIKE CALL SIGN. THERE WERE MANY FOREIGN CARRIERS THAT HAD LIKE SOUNDING CALL SIGNS. I SUGGESTED THAT WE USE THE FLT PHONE AND CALL THE SUPVR OF ZLA. I DID THIS AND TALKED TO A SUPVR. HE KNEW NOTHING OF THIS AND SAID THAT WE WERE CLRED OF ANY ISSUE AND THAT HE WOULD LOOK INTO THE INCIDENT AND SEE IF THERE WAS A KNOWN PROB; AND THAT NO RPT WAS GOING TO BE ISSUED. AS A RESULT OF THIS; I TOLD THE CAPT EVERYTHING THAT WAS DISCUSSED AND CONFIRMED THAT NO ACTION WAS GOING TO BE TAKEN BY ZLA. THIS WAS A VERY UNUSUAL CIRCUMSTANCE FOR ZLA. BOTH THE CAPT AND I HAD FLOWN THIS DEP MANY OF TIMES AND THIS IS A FIRST.