A319 DEP FROM DTW EXPERIENCED CONFLICT AT APPROX 4000 FT AS CTLR ERRED WITH INSTRUCTIONS AND LOST SEPARATION WITH SIMILAR CALL SIGNS INVOLVED.

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WE TOOK OFF ON RWY 4R AT DTW GOING TO SAT. I WAS THE PNF AND THE CAPT WAS THE PF. OUR CLRNC WAS PALACE 2 DEP AS FILED; MAINTAIN 10000 FT. TWR ASSIGNED 010 DEG HDG AND CLRED US FOR TKOF. SHORTLY AFTER TKOF; TWR TOLD US TO CONTACT DEP. DEP TOLD US TO TURN L HDG 185 DEGS; INTERCEPT THE PALACE 2 DEP; AND CONTACT ZOB. I DID NOT CATCH THE ZOB FREQ AND ASKED DEP TO REPEAT IT. WHEN WE CHKED ON WITH ZOB; THEY DID NOT KNOW WHO WE WERE AND TOLD US TO GO BACK TO OUR PREVIOUS FREQ. WE SWITCHED BACK TO DTW DEP AND THEY TOLD US TO LEVEL OFF AT 5000 FT AND TURN R HDG 290 DEGS AND POINTED OUT TFC AT 12 O'CLOCK POS. WE COMPLIED WITH THE INSTRUCTIONS AND CALLED THE TFC IN SIGHT (WE WERE BTWN CLOUD LAYERS AT THIS POINT). DTW DEP GAVE US VECTORS TO THE PALACE 2 DEP AND TOLD US TO CONTACT ZOB. THIS TIME; ZOB WAS EXPECTING US. ZOB GAVE US A PHONE NUMBER TO CALL DTW WHEN WE LAND. AFTER TALKING TO THE TRACON SUPVR; WE LEARNED THAT THERE WAS A SIMILAR FLT NUMBER ON THE FREQ AT THE SAME TIME. THE SUPVR TOLD ME THAT I USED OUR FLT NUMBER DURING MY XMISSIONS AND HE EVEN COMMENTED THAT I QUESTIONED THE FREQ FOR ZOB. WHEN I WAS GIVEN THE FREQ FOR ZOB AGAIN; I SWITCHED OVER. I BELIEVE THAT SOME OF THE FACTORS CONTRIBUTING TO THE LOSS OF SEPARATION WERE: 1) PHASE OF FLT (DEP CLB) A VERY BUSY TIME FOR EVERYONE. 2) WX (IMC) LOW VISIBILITY; LOW CEILING AND IN THE CLOUDS MOST OF THE TIME LEADING UP TO THE LOSS OF SEPARATION. 3) PROBABLY THE BIGGEST CONTRIBUTOR -- SIMILAR SOUNDING CALL SIGNS IN THE SAME AREA AT THE SAME TIME DOING THE SAME THING -- PALACE 2 DEP. I BELIEVE THAT THIS SITUATION COULD HAVE BEEN AVOIDED HAD THERE NOT BEEN SIMILAR SOUNDING CALL SIGNS.