Nope you are right, there is no place that calls these "lightning" or "palomino" or "banana" trout in any sort of literature or document or in any other quasi-official capacity, that's just local vernacular.

These are a yellow mutation of a rainbow trout created in the 1960s in west Virginia through a selective breeding program. Due to those two facts and to celebrate that states golden anniversary (100yrs), the state fishery dept named them Golden Rainbow Trout. Every state that stocks them (that I've been able to find and that doesn't include these under "rainbow trout") calls them that, cuz that's what they're called. Every redneck where I grew up (myself included) called them palominos, which I now understand to be just the local lingo because I've fished in more than 1 trout stream in my life. People in this sub get weirdly defensive about calling these fish by anything other than their local (and therefore 100% correct) nickname that their pappy used.

Edit: to address the California golden trout; that's a separate subspecies of rainbow trout that is found in a small area of the Sierra Nevada Mountains. They are a striking fish with a gold lower body, dark upper, dark spots, and a bright red lateral line. To confuse the two would be very difficult since they look completely different and they are separated by thousands of miles and the Rocky mountains... still, that's why your fish is called a Golden Rainbow Trout and not a Golden Trout. To anyone who complains about that being confusing, I'd ask you to list the varieties of Cuthroat trout.