I remember when I was ten years old having a small collection of trout flies (which I never got to use, since the only places I could go troutfishing were brooks closely overgrown with small trees and bushes.) The prettiest of them was called Dolly Varden, though I did not find out why until many years later, when I read that it was because she was excessively fond of many bright colors in her clothing.
I now suspect the fly tiers liked the colors of the lure better than any trout ever did.
I'm almost halfway through Barnaby Rudge, and so far all Dolly Varden's color has been limited to a cherry red ribbon on her hat.
I searched for picture of Dolly Varden trout flies but couldn't find any. I was surprised to learn that "Dolly Varden" is also a variety of trout. I wonder which came first.

>Dolly Varden (salvelinus malma) are not a true trout, but a member of the char family like Arctic char and bull trout. They look almost exactly like bull trout, but their life history is much closer to that of the Arctic char. In fact, these three species are so closely related, that anglers and scientists have confused the species for decades!<

(click here for more, and pic)
http://fishing-guides.gordonsguide.com/dolly-varden-fishing.cfm

Now, as for whether the fly or the fish captured the nomenclature first. I would surmise that flies tied tto catch Dolly Varden trout assumed the name. BUT, there is a chance that certain colorful flies, in general, were named after the Dickens character without specifically being targeted for the fish of the same name, just because the flies were colorful patterns.