Interesting concept. But I doubt that the Bronx, Queens and Brooklyn would agree to being lumped with Manhattan or that Staten Island would continue as a borough within New York.
If anything should be named Appalachia, it should be West Virginia, and the current Appalachia should be named something more to do with the grassy plains and forests of the southern Ohio river valley and Tennessee river valley.
Also Puerto Rico gains independence, Guam and the Northern Mariana Islands become part of Palau, and the US Virgin Islands become part of the British Virgin Islands.
Maine, New Hampshire, Vermont, and Utah get left alone. Realistically, jettison Southern Maine and Southern New Hampshire into Massachusetts where they belong. What's left of New England can happily join Canada.
Can we get the Populations? Appalachia would work better for WV and the current area could become Kentucky, or Tennesee or some name for both. I propose Allegheny for Erie.