ACR X; WRONG CALLSIGN RESPONSE; UNAUTH DSCNT FROM ASSIGNED ALT; HAD LTSS FROM ACFT BELOW.

Narrative

ACR X WAS LEVEL AT FL240 ON THE SWEED. SWEED2 ARR INTO CINCINNATI ARPT INBOUND TO SWEED INTXN FROM HENDERSON VOR. INDIANAPOLIS CTR INSTRUCTED OUR COMPANY IDENTIFICATION AND FLT NUMBER TO DSND AND MAINTAIN FL 200. THE FO READ BACK THE CLRNC WITH OUR COMPANY CALL AND FLT NUMBER PRECEEEDING THE ASSIGNED ALT OF FL 200. THE FO DIALED THE ALT OF FL 200 INTO THE MCP PANEL AND I ACKNOWLEDGED THE ASSIGNED ALT; AND BEGAN A VERT SPD DSCNT OF 1000 FPM FROM FL 240 TO FL 200. AT FL 23.7 WE RECEIVED A TCASII TA OF AN ACFT 700 FT IMMEDIATELY BELOW US AND DRIFTING TO OUR R. THIS WAS FOLLOWED IMMEDIATELY BY A RA FROM THE TCASII. I ARRESTED THE 1000 FPM VERT DSCNT; AND WE LEVELED BTWN FL 23500 AND 23600. AT THIS TIME INDIANAPOLIS CTR ASKED US WHAT OUR ALT WAS; AND WE RESPONDED. INDIANAPOLIS CTR ADVISED US WE WERE THEN TO MAINTAIN FL 240. WE ADVISED THE CTLR HE HAD ASSIGNED US TO DSCND AND MAINTAIN FL 200. THE CTLR RESPONDED THAT HE HAD ASSIGNED FL 200 TO ANOTHER ACFT AND ADVISED TO LISTEN UP AS THE CALL SIGNS WERE NOWHERE SIMILAR. WE ADVISED HIM WE READ BACK OUR CLRNC; COMPANY NAME AND FLT NUMBER; AND CLBED BACK UP TO FL 240. BOTH THE COPLT AND MYSELF CONCUR IN OUR READBACK AND CLRNC; AND BOTH CONCUR THAT THE ATC CTLR ASSIGNED OUR FLT INCORRECT AND CONFLICTING ALT THAT WAS MEANT FOR ANOTHER ACFT.