A B737-200 FLC DSNDED BELOW THE ASSIGNED ALT NEAR HCM VOR AND RECEIVED A TCASII TA.

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WHILE DSNDING ON THE TERKS 2 ARR TO ORF IN HVY RAIN WITH CONTINUED LIGHT TURB; WE ACCEPTED A CLRNC TO CROSS HARCUM AT 10000 FT. THE CTLR HAD A HVY WORKLOAD AND TURB BELOW FL310 HAD NUMEROUS ACFT ASKING ABOUT RIDE INFO AND REQUESTS FOR LOWER ALTS. WE FIRST WERE CALLED BY A TRANSPOSED CALL SIGN. AFTER QUESTIONING THE CTLR; WE READ BACK; 'CROSS HARCUM AT 10000 FT.' BOTH PLTS POINTED TO THE MODE CTL ALT OF 10000 FT AS PER COMPANY PROC. I WAS THE PF AND STARTED A GRADUAL DSCNT OF APPROX 1200 FPM. AT ABOUT 13000 FT; GOT A TA ON TCASII. SHORTLY THEREAFTER; WE WERE ASKED BY THE CTLR TO 'SAY YOUR ALT.' WE RESPONDED; AND WERE TOLD THAT WE HAD NOT BEEN GIVEN LOWER THAN 14000 FT AND TO CLB BACK TO 14000 FT. THIS WAS NOT A GOOD FEELING. WE CLBED UP TO 14000 FT AND STATED THAT WE HAD IN FACT BEEN GIVEN LOWER AND HAD READ THAT CLRNC BACK. I AM CONVINCED THAT WE READ BACK 10000 FT AND VERY SURE THAT WE WERE GIVEN 10000 FT. INITIALLY CALLING US BY THE WRONG CALL SIGN WAS PROBABLY A FACTOR. ZDC WAS VERY BUSY. THE CTLR ADMITTED THAT HE HADN'T IN FACT HEARD OUR READBACK. WHEN ASKED IF THERE HAD BEEN A CONFLICT; HE REPLIED THAT HE HAD TAKEN CARE OF IT.