Iowa remains a fast battleship, not a battlecruiser

Should Iowa be called a battlecruiser while her later sisters count as fast battleships because of armor differences?

No; every Iowa-class ship was a fast battleship, although the design lies toward the battlecruiser end of that spectrum.

Speed and armor balance can make a fast battleship resemble a battlecruiser without changing its fundamental type. The Iowa class sits toward the battlecruiser end of the fast-battleship spectrum because high speed receives unusual emphasis. That does not erase the protection, armament, or battle-line role that define the design as a battleship. All four sisters remain variations of one fast-battleship design rather than different categories.