During the 1930s the industrial design profession was clawing its way into viability. One device pioneering practitioners such as Norman Bel Geddes and Raymond Loewy relied on was flashy, self-funded designs intended to catch the eye of newspaper and magazine editors.
And those days were the era when modernistic design often incorporated streamlining as a theme. It even reached the point where Loewy came up with a streamlined pencil sharpener.
If aircraft and pencil sharpeners could be streamlined, then why not battleships? After all, streamlining could lead to either faster speeds or more efficient cruising, depending on the situation. And maybe streamlined cladding, if done right, might deflect enemy shells.
Otto Kuhler, best known for his streamlined locomotive designs, did the battleship design shown above as a just-for-the-hell-of-it proposition.
This, from a 1941 Revere Copper and Brass advertisement, is another version of a streamlined battleship. I don't know who designed it.
The problem is, whatever advantages streamlining might offer, the examples shown here would not have been combat-worthy in World War 2.
In terms of armament, they are more similar to the pre-Great War USS Florida (BB-30) shown here than to World War 2 equivalents. American battleships of 1912 vintage were spare designs with turreted main batteries and smaller, anti-torpedo boat guns mounted in the hull. The tall cage masts supported observation compartments where spotters noted where shells were hitting and passed aiming corrections to fire controllers below. Florida's masts also supported searchlight batteries. Aside from the masts and related equipment, the newly-operational Florida could have been streamlined in the Kuhler manner had that concept occurred to naval planners and architects in those days.
This is the USS South Dakota (BB-57), commissioned in 1942. When new, its topside bristled with anti-aircraft guns and more and more were added as the war progressed. Streamlining is clearly antithetical to the need for strong protection from aerial attack.
I'm no naval architect, so I'll only note that the design in the Revere ad has a hull shaped more like that of a powered yacht than those of fast battleships of the early 1940s which featured a more vertical prow near and below the waterline.
Another problem is that the turret armament is impractical. In the first place, five real guns couldn't be fitted into those turrets. In the second place, five guns would make for extremely awkward ammunition handling even if that many guns could be crammed in.
Those streamlined battleship designs were never anything but futuristic fluff. Yet streamlining was in the air in the late 1930s and the notion might have been briefly considered by a few naval planners. If it had, then it was quickly rejected in the interests of practicality under combat conditions.