Artists, maybe among the ground crew would paint the nose art, remember the services had people from all walks of life, some were amateur painters, but some were professionals and were paid to pain the planes, I found this article: http://www.warhistoryonline.com/war-articles/don-allen-nose-art-artist-of-world-war-ii-featured-in-documentary.html

The name would usually be picked by the captain, sometimes after a girlfriend 'back home' (e.g. Memphis Belle) or just a fantasy girl.

Fighter aircraft would typically be painted as a dangerous animal, like a shark or similar.

At the time the art was considered as a morale booster and was allowed, previously it had been discouraged or even banned.

In the biography Unbroken by Hillenbrand, which is about Louis Zamperini, who served on such a plane, Zamperini explains that one day an artist came to paint the art on the plane. In that case the crew chose the name ("Superman") and picture amongst themselves after a bit of debate. I wonder if in some cases the ranking officer chose, though. After all, the 2 most famous bombers of World War 2 are the Enola Gay, named after the mother of the pilot, and Bockscar, named after the captain.