I would simply call it the Boston Metro Area...

mainly because I don't think we'll notice much of a difference

Shooty McPewPew Wastes

Or just The Wasteland.

I have also, though one single descriptor doesn't seem to really fit the variety of areas we know of now,

For starters we've glimpses of...

Scollway Square

Diamond City

The Harbor/Waterfront (my knickname is "the Boomdocks")

Historical District including Museum of Freedom

Lot's more areas to be learned of obviously

e.g. "The Glowing Sea" is probably a whole different area to roam, likely requiring different preparation

Dwight.

Simply refer to it as... "Rainbow."

The City of New Boston in the Commonwealth.

It's called the Cahminwealth. Or at least that's how the locals pronounce it.