B757 FLT CREW PROGRAMMED AND INITIALLY FLEW THE WRONG TRANSITION FOR THE KENNEDY ONE DEP.

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PDC ASSIGNED JFK DEP; BREEZY POINT CLB. CAPT LOADED FMC. THEN; A RWY CHANGE ENSUED; FORCING A RELOAD OF THE DEP. I NOTED THE SID; AND DID NOT REALIZE AN ERROR IN PROGRAMMING HAD BEEN MADE. THE FMC SHOWED A POINT THAT I HAD NOT SEEN BEFORE OR AFTER CRI; INDICATING A PROGRAMMING CHANGE. I ASKED THE CAPT ABOUT IT. HE SAID THAT WAS WHAT THE BOX LOADED WHEN HE SELECTED THE DEP. I RECHKED THE SID; AND SAW WHAT I WANTED TO SEE -- THE RADIAL THE BOX INDICATED; WHICH I THEN EXTENDED THE RADIAL WITHOUT QUESTIONING IT. WE TOOK OFF ON RWY 31L AND CROSSED CRI VOR; AND WERE IN THE TURN TO INTERCEPT THE OUTBOUND RADIAL WHEN DEP TURNED US TO A 250 DEG HDG. THEN ATC QUERIED US AS TO OUR ASSIGNED DEP. WE RECHKED THE SID AND REALIZED SOMEHOW THE CANARSIE CLB WAS IN THE BOX; AND NOT THE BREEZY POINT CLB. WE HEARD NOTHING FURTHER ABOUT IT FROM ATC. WE CHKED THE FMC PROGRAMMING; USING THE ROUTE 2 FUNCTION; AND CAME TO UNDERSTAND THAT THERE MAY HAVE BEEN A RECENT CHANGE IN FMC PROGRAMMING THAT CAUGHT US. WHEN THE PLT SELECTS THE JFK DEP; 2 TRANSITIONS ARE LISTED. ONE IS CRI. BREEZY POINT CROSSES CRI; AS DO MOST THE JFK CLBS; AND SO THE CAPT SELECTED IT. THAT LED TO THE WRONG FOLLOWING RADIAL BEING LOADED. IN ADDITION; THE FIX THAT NOW APPEARS AS AN ALTERNATE SELECTION TO CRI AS A TRANSITION POINT IS NEW. NORMALLY; SID TRANSITIONS APPEAR ON OUR FLT PLAN; AND CUES THE PLT ON WHAT TO SELECT. THIS FIX IS NEW; AND WE WENT WITH THE FAMILIAR FIX THAT WE KNEW WE HAD TO CROSS: CRI. A SIMPLE SUGGESTION WOULD BE TO RENAME THE JFK SID TRANSITIONS; SELECTABLE BY THE PLT; TO EITHER THE DESIRED RADIAL OUTBOUND FROM CRI; OR TO THE ACTUAL CLB 'NAME.' OR; PUT THE TRANSITION FIX IN THE FLT PLAN.