FLC OF AN ISRAEL IA 1123 WESTWIND; TOOK OFF IN RESPONSE TO AN SEL CESSNA SIMILAR SOUNDING CALL SIGN.

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WE CALLED ILG GND FOR A TAXI CLRNC FOR WESTWIND NXXXX FOR A VFR FLT NW TO LNS ARPT. WE WERE TOLD TO TAXI TO RWY 1 AND HOLD SHORT OF RWY 32. AS WE APCHED RWY 32 WE WERE GIVEN FURTHER TAXI INSTRUCTIONS TO TAXI TO THE APCH END OF RWY 1 FOR FULL LENGTH DEP AND SWITCH OVER TO TWR FREQ. AS WE APCHED RWY 1 I GAVE CTL OF THE ACFT TO THE FO AND PUSHED THE SWITCH FOR TWR FREQ. I THOUGHT THE TWR SAID 'NXYY CLRED FOR TKOF L TURNOUT.' AS THE ACFT LINED UP ON THE RWY AND THE TKOF CHKS WERE COMPLETE; I SAW A CESSNA SINGLE ROTATE JUST W OF RWY 1 ON RWY 9. I THOUGHT THIS WAS UNUSUAL AND KEPT MY ATTN ON THAT TFC. AS WE ROTATED AND RETRACTED THE GEAR; WE PASSED BEHIND THAT CESSNA TFC. THEN TWR CALLED TO ASK US 'WHO CLRED YOU FOR TKOF?' I REPLIED; 'YOU DID.' THEY SAID THEY DID NOT. A LATER CALL TO TWR REVEALED THAT WHEN I CHANGED OVER TO TWR FREQ I HEARD THE TWR CLR THE CESSNA TO GO WITH L TFC AND THAT THE OTHER ACFT HAD A SIMILAR CALL SIGN 'XY' AS OPPOSED TO 'YX.' I FEEL THAT HAD WE BEEN ISSUED A DEFINITE 'HOLD SHORT OF RWY 1' CLRNC THIS EVENT MIGHT NOT HAVE HAPPENED. IT ALSO POINTS OUT THE NEED TO PAY CLOSE ATTN TO RADIO INSTRUCTIONS AND ASK FOR CONFIRMATION IF THERE IS ANY DOUBT.