A DEP BEECH JET FLT CREW OVERSHOOTS THEIR ASSIGNED ALT OF 4000 FT DURING A CLRNC MIX-UP WITH THE PCT DEP CTLR 2 MI SW OF BWI; MD.

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WE DEPARTED 2 ACFT BEHIND AN ACFT WITH SIMILAR CALL SIGN OUT OF BWI; ON RWY 15L. WE WERE GIVEN A VECTOR FOR A CLBING R TURN TO A HEADING OF 320 DEGS; AND TO 4000 FT. WE WERE IN OUR CLBING TURN AND WERE TOLD TO CONTACT DEP. UPON CALLING; THE DEP CTLR GAVE THE OTHER ACFT A VECTOR FOR A L TURN TO 280 DEGS AND A CLB TO 14000 FT. WE MISTOOK THE CALL TO BE FOR US. MY COPLT REPLIED THAT WE WOULD STOP OUR TURN AT 280 DEGS AND CLB TO 14000 FT. THE CTLR REPLIED THAT THE CALL WAS NOT FOR US; BUT FOR THE OTHER ACFT AND TO LISTEN MORE CLOSELY (AMONG OTHER THINGS). WE KEPT THE TURN GOING TO A HEADING OF 320 DEGS; WHILE TRYING TO VERIFY THAT WE WERE TO CLB TO 14000 FT. WE WERE PASSING OUR ORIGINALLY ASSIGNED ALT OF 4000 FT WHEN THE CTLR TOLD US THAT WAS NOT OUR ALT; AND SINCE WE WERE ALREADY THROUGH 4000 FT; TO CONTINUE THE CLB TO 6000 FT. WE HAD MISTAKEN A CALL FOR US THAT WAS REALLY FOR A SIMILAR SOUNDING ACFT. IT COULD HAVE BEEN A PROB IF THERE HAD BEEN ANOTHER ACFT ABOVE US; BUT IN THIS INSTANCE IT WAS NOT A FACTOR. WE NEEDED TO LISTEN MORE CAREFULLY TO CALL SIGNS FROM CTLRS; ESPECIALLY WHEN WE KNOW SIMILAR SOUNDING ACFT IS IN THE AREA. THE CTLR COULD HAVE HELPED THE PROB BY NOT GOING IN SO MUCH DEPTH TO 'CHEW US OUT' AT THAT MOMENT. BY DOING SO; WE WERE UNABLE TO GET OUR CALLBACK INTO HIM TO VERIFY THE ALT WE WERE SUPPOSED TO BE AT. IF HE WOULD HAVE JUST LET US KNOW THE CALL WASN'T FOR US; AND MAYBE A SHORT; 'LISTEN UP;' WE COULD HAVE GOTTEN OUR CALL INTO HIM TO VERIFY THE ALT WE WERE TO BE AT. THEN WE COULD HAVE LEVELED OFF AT OUR ALT AND HEADING WITH NO FURTHER PROB.