FLC OF ACR MLG ACFT INADVERTENTLY RESPONDED TO ATC INSTRUCTIONS TO ANOTHER ACFT WITH THE SAME CALL SIGN BUT DIFFERENT COMPANY NAME SINCE CTLR DID NOT USE THE OTHER COMPANY NAME IN HIS XMISSIONS OR ACKNOWLEDGE THE COMPANY NAME USED BY THE RPTING ACFT.

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WHILE CRUISING AT FL350; J-18; ABOUT 60 MI E OF GCK VOR; ZKC SAYS COME L 5 DEGS AND PROCEED DIRECT LVS VOR WHEN ABLE. ALMOST AS SOON AS WE TURN TO THE NEW HDG; CTR SAYS COME R 10 DEGS FOR TFC; WHICH WE DO. AFTER ABOUT A MIN ON THIS HDG; CTR SAYS DSND AND MAINTAIN FL310; EXPEDITE THROUGH FL330; WHICH WE DO; ALTHOUGH NO TFC IS OBSERVED ON TCASII. AFTER COMMENCING THE DSCNT; CTR ADVISES THAT HE IS NOT PICKING UP OUR ALT READOUT AND TO CALL HIM OUT OF FL330 WHICH WE DO. WE TOLD HIM WE WERE LEVEL FL310 AND HE THANKED US FOR THE DSCNT AFTER WHICH HE GAVE US A HDG FOR LAMAR VOR. WE ADVISED HIM THAT WAS NOT ON OUR RTE OF FLT; AND THEN HE ASKED US WHERE WE WERE GOING. WE RESPONDED THAT WE WERE ENRTE TO TUCSON TO WHICH HE REPLIED THAT WE COMPLIED WITH ANOTHER CARRIER'S DSCNT INSTRUCTIONS WITH THE SAME FLT NUMBER. I LATER TOLD HIM WE HAD NEVER HEARD HIM CALL THE OTHER CARRIER'S CALL SIGN. HE RESPONDED EXPLAINING THAT THE OTHER CARRIER HAD NOT CHKED IN ON HIS FREQ YET. THIS COMPLETELY CONFUSED ME BUT I GUESSED THAT HE HAD FORGOTTEN THAT FACT OR HAD ASSUMED HE HAD CHKED ON. ANYWAY; ALL OF OUR XMISSIONS WERE MADE USING OUR COMPANY NAME AND FLT NUMBER. THE CTLR WAS LEAVING OFF THE COMPANY NAME AND SINCE WE WERE TALKING SO FREQUENTLY WITH HIM; WE DID NOT VERIFY THE COMPANY HE WAS CALLING AND HE WAS NOT PICKING UP OUR COMPANY NAME IN OUR XMISSIONS. WE BOTH SHOULD HAVE MADE MORE CERTAIN OF OUR CALL SIGNS. SUPPLEMENTAL INFORMATION FROM ACN 241330: THE CTLR SAID THE OTHER CARRIER HAD NOT CHKED ON THE FREQ AND THAT WHEN ACKNOWLEDGED HIS CLRNCS FOR THE TURN AND DSCNT; HE THOUGHT IT WAS THE OTHER CARRIER RESPONDING. THIS CTLR SHOULD HAVE ADVISED US OF THE SIMILAR CALL SIGN COMING ONTO THE FREQ; AND SHOULD HAVE PAID EXTRA ATTN TO USING THE PROPER CARRIER NAME.