All extant “penguins” (I call them sphenicids to sound smarter and be more accurate) are allegedly named after the penguin, a species of extinct Great auk. People knew about both taxa for a long time, but from what I’ve heard the term was applied to the Great auk before sphenicids got the name. Correct me if this is wrong.
The wasp mantidflies (Climaciella) are neither wasps nor mantises but are instead in Neuroptera with other mantisflies/mantidflies, owlflies, lacewings, etc.
Cathartes aura is known as the turkey vulture, and the scientific name for the turkey species we know and love is Meleagris gallopavo, which roughly translated means guineafowl fowl-peacock (Linnaeus tried really hard on this one).
Buteo jamaicensis is sometimes called a chicken hawk (I give myself half credit because “hawk” is in the name and describes the bird accurately), but it is better known in my part of the country as the red-tailed hawk.
Hippopotamus (“hippo-” = horse). Bullfrog. Tapir frog. Wolverine. Owlet moth. Aardwolf. Koala bear. Meerkat. Maned wolf. Jellyfish, starfish. Tufted titmouse. Sea dragon. Sea rabbit. Electric eel. Pigeon horntail. Horny toad. Vampire squid (genetically closer to octopus). Wolf eel. Giraffe weevil. Muskrat.
Lionfish, catfish, batfish, frogfish, toadfish, zebrafish, scorpionfish, dragonfish (half credit because we don’t consider Komodo dragons as dragons), seahorse.
Bull shark, tiger shark, lemon shark, leopard shark, salmon shark. Spiny dogfish. Eagle ray. Saw shark (genetically closer to rays than sharks).
Mountain goat and muskox (time for a better name for both of these cool ungulates!).
Sun spider or wind scorpion for all solifuges.
Elephant shrew (neither elephant nor true shrew). Naked mole rat (neither genetically close to true moles nor to rats). Tiger bee fly (neither a tiger nor a bee, half points for being a fly). Hummingbird hawkmoth.
Anything marsupial + (name for a placental mammal here, examples include lion, tiger, rat, mouse, porcupine). Any something-bug that is not in Hemiptera and any something-fly that is not in Diptera.
I don’t know if anemones the plants or anemones the animals were named first, but one has to be named after the other.