LEAR 45 FLT CREW HAS SIMILAR CALL SIGN TO ANOTHER COMPANY ACFT. DURING CRUISE; ATC ISSUES A FREQ CHANGE TO THE FLT CREW AND THE OTHER ACFT ACCEPTS THE CHANGE. ATC CTLR DOES NOT CATCH THE MISTAKE.

Narrative

WE (ACFT X; N-XXYY) DEPARTED MANKATO; MN (MKT) TO DALLAS LOVE ARPT (DAL). WE WERE AT FL400 AND ON A KANSAS CITY ENRTE FREQ; APPROX 70 MI N OF TUL VOR. I HEARD ANOTHER CPR JET (ACFT Y) CALL ONTO THE FREQ. I EXPECTED THE CTLR TO POSSIBLY ADVISE THAT WE (A SIMILAR SOUNDING CALL SIGN) WERE ALSO ON THE FREQ -- IT DIDN'T HAPPEN. THE FREQ WAS FAIRLY BUSY; SO I DIDN'T SAY ANYTHING TO INTERRUPT. ABOUT 5 MINS LATER; THE KANSAS CITY CTLR ISSUED A FREQ CHANGE TO ACFT Y; N-XYY. THEY ACCEPTED THE CHANGE AND LEFT THE FREQ. AS WE FLEW OVERHEAD TUL AND CHANGED HDG TO BEGIN THE FINGR 3 ARR INTO DAL; THE ENRTE CTLR GAVE US A TA FOR AN AIRPLANE AT FL360. I THOUGHT THAT WAS KIND OF STRANGE SINCE WE WERE 4000 FT HIGHER. I ASKED THE CTLR IF THE EARLIER FREQ CHANGE FOR ACFT Y MIGHT HAVE BEEN FOR US (ACFT X) INSTEAD. HE SAID; 'NO; STAY WITH ME.' WE WERE THEN GIVEN A DSCNT TO FL360 AND A SUBSEQUENT FREQ CHANGE TO ANOTHER KANSAS CITY FREQ; WHO GAVE US A FURTHER DSCNT TO FL240 AND REQUESTED AN EXPEDITED DSCNT. PASSING FL285; THE CTLR ASKED OUR ALT AND REQUESTED A FASTER DSCNT TO BE BELOW FL270 IN 30 SECONDS. WE COMPLIED; BUT I SAW ABSOLUTELY NO OTHER ACFT IN OUR VICINITY ON THE TCAS. WE WERE THEN GIVEN A DSCNT TO 16000 FT; A FREQ CHANGE TO 'ZME' AND HE GAVE ME A FURTHER DSCNT TO 5000 FT. I KNEW THEN THEY HAD MIXED US UP WITH THE OTHER AIRPLANE AND QUERIED THE MEMPHIS CTLR. HE ASKED MY POS -- APPROX 25 MI E OF MCALESTER VOR (MLC) ON THE FINGR 3 ARR TO DAL. HE TOLD ME TO RETURN TO THE PREVIOUS FREQ AND A LEVELOFF AT FL190. BY THIS TIME; THE CTLRS HAD FIGURED OUT WE WERE GOING TO DAL AND THE OTHER ACFT WAS GOING TO HARRISON; AR (HRO). THE CTLR GAVE ME A TELEPHONE NUMBER AND ASKED ME TO CALL THEM LATER. THE SUPVR SAID THERE WERE NO CLOSE CALLS AND NO SERIOUS SITUATIONS DEVELOPED BECAUSE OF THIS; BUT THEY WANTED TO ELIMINATE THINGS LIKE THIS FROM HAPPENING AND AVOID SERIOUS SITUATIONS IN THE FUTURE.