A B757 FLT CREW GETS A WRONG FREQ ASSIGNMENT AND SUFFERS A HDG TRACK DEV DEPARTING MIA; FL.

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ON DEP FROM MIA ON RWY 9L; TWR SENT US TO DEP ON FREQ 119.45. THE FREQ WAS VERY BUSY AND I WAS NOT ABLE TO IMMEDIATELY CHK IN. ON INITIAL CALL; DEP IMMEDIATELY CAME BACK VERY FAST WITH A CLRNC TO TURN TO 270 DEGS; MAINTAIN 250 KTS; CLB TO 16000 FT AND CHANGE FREQ TO MIA ON 13..... I DIDN'T GET IT ALL THE FIRST TIME AND ASKED FOR THE FREQ AGAIN. BOTH TIMES I INCLUDED ACR FLT NUMBER IN MY COMS. WE CHANGED FREQS. THE NEW CTLR SAID WE WERE ON THE WRONG FREQ AND TO GO BACK TO DEP. WE WENT BACK. DEP ASKED US WHO CLRED US TO 16000 FT. I SAID THAT HE DID. HE TOLD US TO STAND BY. HE THEN CLRED US TO 16000 FT; 250 KTS; 360 DEG HDG TO INTERCEPT THE HEDLY TRANSITION AND GO TO ANOTHER FREQ AND TELL THEM OUR SPD. WE DID THIS AND CONTINUED THE DEP. NOTHING WAS SAID ABOUT AN ERROR OR PROB BY THE CTLR. WE'RE NOT SURE THERE WAS ONE. IT WAS HIS QUESTION THAT MADE US ASK OURSELVES IF THERE WAS A PROB. THERE MAY HAVE BEEN CONFUSION BY THE DEP CTLR AND OURSELVES AND OTHERS AS COMPANY FLT WAS JUST IN FRONT OF US AND ANOTHER COMPANY FLT WAS ON THE NEXT FREQ. THERE SEEMS TO BE AN INCREASING FREQ OF SIMILAR CALL SIGNS IN THE SAME SECTORS AT THE SAME TIME OVER THE PAST FEW MONTHS. CAN SOMEONE LOOK INTO THE SIMILAR CALL SIGNS ISSUE?