B737-300 CREW HAD THE CTLR CONFUSE SIMILAR CALL SIGNS AND DID NOT CONFIRM THE CLRNC WHEN THE CREW QUESTIONED IT.

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ATC MISCOM/NAV. ON DEP FROM BALTIMORE; I WAS THE PF. DEP CTL GAVE US RWY HDG INITIALLY ON OUR DEP FROM RWY 28. DURING OUR CLB WE WERE GIVEN CLB CLRNC TO 10000 FT. JUST AS WE LEVELED AT 10000 FT; THE CTLR TOLD US TO 'TURN R HDG 140 DEGS' AND THEN GAVE US A FREQ CHANGE. SINCE A R TURN TO 140 DEGS WOULD HAVE BEEN MORE THAN A 180 DEG TURN; WE ASKED FOR CONFIRMATION USING OUR FULL CALL SIGN. THE CTLR CONFIRMED THE CLRNC. WE BEGAN THE R TURN AND ESTABLISHED CONTACT WITH THE NEXT CTLR; WHO IN TURN TOLD US THAT WE HAD BEEN GIVEN THE WRONG FREQ; AND HANDED US OFF TO A THIRD CTLR. THE THIRD CTLR SAID THAT WE HAD 'TAKEN SOMEONE ELSE'S VECTOR' WHO HAD A SIMILAR CALL SIGN. WE WERE THEN VECTORED BACK ON COURSE WITH NO FURTHER COM ON THE ISSUE. TO MY KNOWLEDGE; THERE WERE NO TFC CONFLICTS. BOTH THE CAPT AND I ARE SURE THAT OUR CALL SIGNS WERE READ BACK PROPERLY AND VERY CAREFULLY WHEN WE CONFIRMED THE CLRNC. I BELIEVE THAT IT IS IMPORTANT TO ADJUST THE SCHEDULED FLT NUMBERS IN SUCH A WAY AS TO NOT HAVE 2 VERY SIMILAR CALL SIGNS (IE; COMPANY ABC AND COMPANY DABC) IN THE SAME REGION AT THE SAME TIME THUS REDUCING THE CHANCE OF A PLT OR CTLR CONFUSING 2 AIRPLANES.