Fractional Captain reported Clearance Delivery incorrectly spelled out NECKK instead of the correct waypoint NECCK and along with Colts Neck VOR being decommissioned; led the flight crew to make a wrong turn on departure.

Narrative

For the EWR - ZZZ reposition I had to call Clearance Delivery for the clearance as it was completely different than the filed flight plan. Clearance gave the EWR 5 Departure; vectors Colts Neck then said Colts Neck was decommissioned and the fix was NECKK (he spelled it out) then direct ZZZ. I read back the clearance and spelled out the fix as it was given to me and there was no change or correction to my readback.I entered the clearance into the FMS. We confirmed the FMS fixes then continued with checklists etc. We departed 22R and were handed off to Departure. He cleared us to Colts Neck and I said cleared to NECKK confirming our fix clearance since Colts Neck was decommissioned (as stated by Clearance Delivery). NECKK was about a 30-degree right turn. Departure queried wondering why the right turn and said he expected a left turn. I responded saying we were direct NECKK and spelled it out. He had us make the left turn and vectored us in the correct direction and I asked if that spelling was correct and he said he had to look for it also. I found the error shortly after and asked if it was NECCK to which he confirmed. I told him I had missed a letter. We were cleared direct to NECCK and flew on without further issue to ZZZ. There were no traffic conflicts or any other deviations other than that navigation error. Suggestions: I don't know when Colts Neck was decommissioned but it seemed to cause a bit of confusion even to the controllers. Clearance Delivery gave me the spelling which I read back as given (error #1); we confirmed the fix in the box - the only fix but I missed the distance to the fix being too far (#2); I missed confirming the total distance in the PROG page (#3); made a wrong direction turn (#4); the Departure Controller also was somewhat confused by the fix instead of Colts Neck.The first error set in motion the classic Swiss cheese error model. I had a couple of opportunities to catch the error and missed. Confirming the box and the total distance are things I don't usually miss but I did this day. Reminding ourselves to slow down and eliminate the errors regardless of where the errors originate is imperative.