HDG TRACK DEV PICKED UP BY BUSY BUT ALERT ARTCC RADAR CTLR.

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WE WERE IN OUR DEP CLB FROM BOSTON LEAVING FL270 FOR FL390 BEING VECTORED W TOWARD OUR FILED RTE OF GLIDE; BAF J77 BWX; ETC. THERE WAS A LULL AND I BEGAN THE PAX PA WHICH HAD BEEN DELAYED UNTIL THIS TIME. DURING THE PA CENTER CALLED; CLRED US TO FL390; AND DIRECT TO BARNES. I INTERRUPTED THE PA; RESPONDED TO THE CLRNC. THE CAPT UPDATED THE ALT AND REPROGRAMMED THE FMC. I FAILED TO NOTICE THAT HE SELECTED BWZ WHICH IS BROADWAY RATHER THAN BAF WHICH WAS BARNES. I RESUMED MY PA. CENTER THEN CALLED AND ASKED IF WE WERE PROCEEDING DIRECT BARNES. I LOOKED AT THE SCREEN AND SAW BWZ. IT DIDN'T CONNECT THAT WAS BROADWAY RATHER THAN BARNES. I RESPONDED ROGER WE WERE PROCEEDING DIRECT BARNES. SHE IMMEDIATELY RESPONDED NEGATIVE; I SHOW YOU 10 MI S OF BARNES HEADED TOWARD SPARTA (SAX) (WHICH WAS ON A DIRECT COURSE FOR BWZ). I REALIZED THE ERROR THEN AND ROGERED HER ESTIMATE OF OUR POS. SHE THEN GAVE US A WESTERLY HDG; TOLD US TO LEVEL AT 310 AND HANDED US OFF TO ANOTHER CTLR. 2 PROBLEMS CONTRIBUTED TO OUR MISTAKE. 1 WAS THAT THE CLRNC USING THE NAME RATHER THAN THE PHONETIC SPELLING LED TO THE ENTERING OF BWZ FOR BARNES. THE SECOND WAS THE FACT THAT I WAS DOING A PA AND CONSEQUENTLY DID NOT XCHK WHAT THE CAPT'S UPDATE OF THE FMC. IT CTLRS WOULD USE PHONETICS IN THEIR CLRNCS IT WOULD HELP. ALSO; DELAYING PA'S UNTIL CRUISE ALT ESPECIALLY IN HIGH DENSITY AREAS.