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The name of the town is actually "Cape May Court House, NJ," so it should be changed to reflect that on supercharge.info. Cape May is just the geographical feature (the southern most point in New Jersey).
I think they're just using whatever Tesla has their marker named as, even if it's not really accurate to the local town/city borders. In this case, Cape May, NJ--without the "Court House". But that may change once the location becomes operational. If so, I'm sure Supercharge.info would change theirs to match.
My wife left there yesterday. She only saw crew there working one day over the week and thought they were probably done with their task and the next sub was on deck. Doubt it will be done and certified in two weeks, but you never know.
I was just down last weekend. I drove by, they are setup 12 stalls but not operational yet. Gotta be very close. Keep checking supercharge.info for updates.