Technically cobras belong to the genus
Naja, but the king cobra is the sole member of the genus
Ophiophagus.
Also...
- Any dinosaur with -saurus in its name it technically incorrectly named as -saurus is Greek for "lizard," and dinosaurs a) weren't lizard, b) weren't closely related to lizard, and c) didn't act like lizards. This is also true for pterosaurs, ichthyosaurs, pliosaurs, plesiosaurs, and many other groups. The only extinct group this is technically is the mosasaurs, as mosasaurs were a type of a marine (and in some cases freshwater) lizard.
- Parasaurolophus, a "duck-billed" dinosaur whose name means "near Saurolophus," was named so because it was originally thought to be closely related to Saurolophus, another "duck-bill," but we now know these two actually belonged to different subfamilies.
- Procompsognathus wasn't closely related to Compsognathus.
- Oviraptor means "egg thief." The genus was named because the holotype was discropvered atop a nest and was thought to of been stealing someone else's eggs when it died. We know now it was actually sitting on its own nest, like a modern bird.
- When people here pterodactyl they picture a Pteranodon but pterodactly actually refers to Pterodactylus, a small fish-eating genus from Germany. Additionally this group of reptiles is often called "flying dinosaurs" despite the fact they're not dinosaurs (although they are closely related).
I'd argue that these names are not incorrect, either technically or practically. From a technical standpoint, any formal scientific name formed following the requirements of the code of zoological nomenclature (e.g., type designated, etymology provided, published, etc.) and predating other valid names for the same entity is the technically correct name for a taxon. From a practical standpoint, they were all correct according to the science of the day and most of them are still not really misleading in any way. For example, while
saurus is usually translated as "lizard" there's no reason to think that ancient Greeks had the same conception of lizard that we do, and others might choose to translate the word as "reptile". The only one I'd call truly misleading is
Oviraptor (though it's still not entirely clear what they ate!).
Nope; it
IS in the larger Elapidae family which also contains true cobras and a variety of other taxa, but it is actually the sister genus to
Dendroaspis, the mambas

and is basal to the clade containing
Naja and related genera.
The "king" epithet refers to the fact that the species is ophiophagus, and preys on cobras and other snakes.
The tricky thing here is that there's no reason a common name needs to denote a monophyletic group. Even taking account of evolutionay history, a reasonable definition of cobras would be "elapid snakes that produce a hood display", meaning king cobras qualify. Heck, that definition could even include mambas, in which case monophyly would be restored.
Overall, there are tons of common names used for paraphyletic groups that are both unambigouous and usefully descriptive -- fish, lizard, monkey, antelope, etc. The trickier situation is when animals are not part of a named group but have that group's name as part of their name -- starfish, jellyfish, elephant shrew, etc. I personally dislike the push to change the common names used for these, but it's probably a losing battle and I suppose in a decade I'll be using sea star, jelly, and sengi without batting an eye.