OFFICIAL name of the island?

[terracore]

People on the East coast call Washington DC "Washington" and they refer to the state of Washington as "Washington state". On the west coast it's the opposite. The state is called "Washington" and the district of Columbia is referred to as "Washington DC". I think something similar is happening here. When I am communicating with another resident I say I live on "the big island". When I am communicating with somebody from the mainland I say I live "On the big island of Hawaii".

New York City is in New York.
Oregon City is in Oregon.
Hawaii county is in Hawaii.
But Kansas City is in Missouri. I don't ask why. I don't want to know. Oops I googled it. Both Kansas and Missouri have a Kansas City. That's OK. There is a Moscow in Idaho.