During WWII, Navy and Marine pilots didn't generally have their "own" plane in the way the AAF guys did. For that matter, Marine SQUADRONS didn't always have their own aircraft, and you would have several VMFs sharing from a pool of machines. Individual pilots might still have had a favored ride, but otherwise they would generally fly whatever aircraft were operable.
I think the carrier squadrons were afforded a bit more luxury in this regard, but in general the squadron's aircraft were shared among pilots and it was rare to have individual machines (VF-17's Corsairs are one of the few examples I can think of where you really see pilots having an "assigned" aircraft).
Even with the AAF pilots, while they would have "their" individual plane, their plane might not always have been available so they would fly whatever was.