A B737-200 FLC LEAVES THEIR LAST ASSIGNED ALT FOR A NEWLY ASSIGNED ALT AS PER ATC INSTRUCTIONS. CTLR THEN ASKS FOR THEIR ALT IN CLB AND REASSIGNS THE OLD ALT TO THEM. CREW CITES A MIXUP IN FLT NUMBERS FROM ATC.

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WE WERE CRUISING AT FL290; PROCEEDING DIRECT TO BRICKYARD (VHP). WE REQUESTED DIRECT TO SHELBYVILLE. ZKC ASKED WHAT OUR AIRSPD WAS TO WHICH WE REPLIED 280 KIAS. CTR CAME BACK WITH INSTRUCTIONS TO CLB TO FL330; MAINTAIN 270 KIAS UNTIL FL310 THEN NORMAL AIRSPD. WE READ BACK THE CLRNC; USING OUR CALL SIGN ACR ABXY; AND BEGAN THE CLB. AT APPROX FL300 CTR ASKED WHAT OUR ALT WAS AND THEN TOLD US TO IMMEDIATELY DSND BACK TO FL290. WE DID THIS AND CONTINUED ON TO CVG. THE CAUSE OF THIS DEV APPEARS TO BE CONFUSION OVER CALL SIGNS. DURING THE WHOLE EXCHANGE BTWN CTR AND OURSELVES DESCRIBED ABOVE WE CONSISTENTLY USED OUR CORRECT CALL SIGN; ACR ABXY. CTR WAS ALSO CALLING US BY ACR ABXY EXCEPT 1 TIME WHEN THEY CALLED US ABXZ. WE HADN'T HEARD ANY OTHER ACFT ON FREQ WITH A SIMILAR CALL SIGN; SO WE ASSUMED HE MEANT ACR ABXY. NO OTHER ACFT RESPONDED TO THE CLB INSTRUCTIONS. AFTER THE EVENT; THE CTLR CALLED AN ACR BAXZ AND GAVE HIM THE CLRNC TO FL330 THAT HE HAD PREVIOUSLY GIVEN US. IT APPEARS THAT WHEN HE CALLED US ACR ABXZ HE MEANT TO SAY ACR BAXZ. SUPPLEMENTAL INFO FROM ACN 398445: THE CLRNC WAS READ BACK A SECOND TIME TO CONFIRM THE ALT AND AIRSPD USING OUR PROPER FLT NUMBER AND WAS AFFIRMED A SECOND TIME USING OUR PROPER FLT NUMBER.