B737-200 CREW HAD ZMA CTLR MIX UP CALL SIGNS. CTLR SHIFT CHANGE WAS TAKING PLACE AT THE TIME.

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WE WERE FLYING ACR X FLT XXXA FROM RSW TO EWR. WE WERE LEVEL AT FL310; JUST N OF SQT NDB. ZMA GAVE US A CLRNC TO FLY HDG 020 DEGS UNTIL RECEIVING ILM; THEN DIRECT ILM. ZMA THEN CONDUCTED A CHANGEOVER BRIEFING BECAUSE WE HEARD IT OVER THEIR HOT MIKE. DURING THE BRIEF; I HEARD THE OUTGOING CTLR BRIEF THE ONCOMING CTLR THAT 'ACR X FLT XXXA WAS GIVEN 020 DEGS UNTIL RECEIVING ILM; BUT THEY HAVE NOT CHKED IN YET.' I WANTED TO CORRECT THE NEW CTLR THAT WE HAD CHKED IN; BUT IT BECAME APPARENT HE WAS BUSY CTLING SEVERAL FREQS. A FEW MOMENTS LATER; I HEARD THE INSTRUCTIONS 'ACR X FLT XXXA; I HAVE SOME PARALLEL TFC; SO FLY HDG 045 DEGS TO INCREASE SEPARATION.' MY CAPT WAS MAKING A PA TO THE PAX; SO I ACKNOWLEDGED 'ACR X FLT XXXA HDG 045 DEGS' AND COMPLIED. I SOON NOTICED THAT ZMA CTLR WAS ALSO CTLING ANOTHER ACR X ACFT ON A DIFFERENT FREQ WITH A SIMILAR CALL SIGN WHICH I BELIEVE WAS FLT XXXB. I WAS CONCERNED THAT; WITH SIMILAR CALL SIGNS AND SIMULTANEOUS FREQS; WE MIGHT HAVE SIMULTANEOUSLY ACKNOWLEDGED A 045 DEG HDG. I WANTED TO VERIFY THAT THE CTLR KNEW I HAD TURNED; BUT I HAD TO WAIT WHILE HE WORKED ANOTHER FREQ. I FINALLY GOT THROUGH TO HIM AND SAID 'MIAMI; ACR X FLT XXXA; I WANTED TO MAKE SURE YOU KNEW THAT WE ARE LEVEL FL310 HDG 045 DEGS.' HE CAME BACK WITH 'ACR X FLT XXXA; FLY HDG 015 DEGS UNTIL RECEIVING ILM.' WE HAD BEEN ON A 045 DEG HDG FOR A COUPLE OF MINS. DURING THE REMAINING TIME WITH THIS CTLR; SEVERAL FLTS ON DIFFERENT FREQS WERE PROBABLY; UNWITTINGLY; CALLING THE CTLR NEAR SIMULTANEOUSLY; AND THIS MADE HIS JOB DIFFICULT. THIS ALSO HAPPENED WHEN WE WERE INSTRUCTED TO CONTACT ZJX. I DID NOT SEE ANY EMERGING CONFLICTS ON OUR TCASII WHILE WE FLEW THE 045 DEG HDG. THE MIA CTLR MADE NO MENTION OF A HDG DEV; IF INDEED THERE WAS ONE. OBVIOUSLY; THE USE OF SIMULTANEOUS FREQS DIMINISHES SITUATIONAL AWARENESS ON THE PART OF AIR CREWS; AND INCREASES CTLR WORKLOAD. WE LISTEN CAREFULLY TO THE RADIOS; USE ACTIVE NOISE REDUCTION HEADSETS TO MITIGATE THE NOISY AMBIENT LEVEL OF THE B737-200 COCKPIT; AND TRY NOT TO XMIT IF WE THINK THE CTLR MIGHT BE BUSY ON ANOTHER FREQ.