They should have named it Kaga or Akagi.
Or, the Yamamoto.
(Naming her Akagi would open a can of maritime tradition worms for her sister. For starters, the historical Kaga was not a true sister to Akagi. Both ships were unique classes. Worse, Kaga is not a proper "cruiser" name. Cruisers are named after unincorporated places, mostly scenic islands (Akagi, "Red Castle", is a volcanic rock off the east coast of Japan). But Kaga is an ancient prefecture, and is thus a battleship name. Tradition is hard to buck, especially in Japan. Then again, they could name their next garbage scow "Musashi"...I'm just guessing here.)