Dragonfly adults are very rarely vulnerable to trout because they are superb at flight, but their large, slow nymphs are welcome food. The adults and nymphs are both impressive predators upon other insects, and I have watched adult dragonflies kill large mayfly duns and tear through a cloud of midges at rate of several per second.
This common name refers to only one order.
These are pretty much always called Dragonflies.
Dragonflies and damselflies are in the same order, Odonata, but they are taxonomically separated on an obscure level not built into this site, the suborder. Dragonflies are in the rarely mentioned suborder Epiprocta, and within that suborder is the infraorder Anisoptera, the scientific name by which they're best known. None of that will help you catch trout, but it explains what the hyphen in this page's name is all about.