It's interesting to note that the "Brooklyn Queens Expressway East" has
reference markers for I-278, which treat it as a sixth segment of such (note the second line). Staten Island is X6M1, Brooklyn is X2M2, Queens is X5M3, Manhattan is X4M4, The Bronx is X1M5, and the east BQE is X5M6.
There is
maybe an argument to be made that this should be in usai as "I-278 (Jackson Heights, NY)" but I dunno.
If in usasf I agree with "BQExpyE". The name in question does not appear on any signs but has consistently appeared on maps over the years, at least.
Exit numbering gives me a little heartburn. There are no numbering collisions, but still. I'd say it counts as >1 sequence.
If there is more than one exit number sequence for a highway and no concurrent route to explain it, suggest a proposal in the forum what parenthetical distinction should be used. All exit numbers in a sequence get the same parenthetical suffix.
I suggest 43(278) for the one. And the other? Oy... 5(Gra) would fit with the other similar styles the manual does recommend for concurrencies.
I think you can get away with 3 point labels:
I-278
43
GraCenPkwy
and that avoids any exit numbering problems. "Exit 5" gets 1PPI'ed in with the last of those 3, and since there is no exit number for the mainline default into the Grand Central Parkway that point doesn't need to be labeled with a number.
As for NY 984J (that's the reference route number for the Hutch-684 connector), well, the option of putting it in usai as "I-684 (Harrison, NY)" is also out there.
Otherwise, yeah, it has neither a signed name nor a common name. If putting this in usasf I'd... frankly I'd just put it in as NY984J, since that's as real as any other of the names you pulled up but likely to be recognized by more people (I certainly know it as "984J" but had no idea any of those other names existed!)