A form of Names to Run Away From Really Fast: People and families can have animals, real and mythological, as part of their names, but in fiction it's usually a dangerous sign to meet someone with a predatory animal in their name. Wolf, dragon, lion, tiger, coyote, snake.
Note that animal names can go either way depending on the setting; they can imply evil, or can simply be used to imply that a character is fierce and dangerous, and as such, can be used for good characters or even heroes. Some animals are tipped more one way than others, of course; lions and wolves can imply nobility, but snakes and scorpions usually don't.
Examples:
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Bear
Most kinds of bear aren't well-known or catchy enough to get their own section, but watch out for anyone who goes by "Grizzly" or "Kodiak". However Russian bears (as a name, nickname, or title) definitely fit in this trope.
Anime and Manga
Fullmetal Alchemist's Briggs Bears. With minds and bodies tempered by the driving cold of the border between Amestris and Drachma (approximate Fantasy Counterpart Cultures of Germany and Russia, respectively), they're a force to be reckoned with.
This trope with a twist: in the Red Dwarf episode "Gunmen of the Apocolypse", one of the denizens of Kryten's western-themed dreamscape was named 'Bear-Strangler' McGee.
Ursa (her name meaning 'she-bear') from Avatar The Last Airbender is an aversion. Despite being the wife of the Fire Lord, she is shown to be a kind and loving mother ...who admittedly killed Azulon, the then-Fire Lord, for threatening the life of her son.
Ursula. The name actually means "little she-bear," but she turns it into a Name to Run Away From anyway.
Karasu (Japanese for crow) from Three of Heart, One of Blood doesn't seem like this at first: He offers to Bring Yukimori back to life. Unfortunately, it doesn't hold, as he's a Legacy and can't raise the dead — but he can cast extremely realistic illusions.
Date Masamune, the One-Eyed Dragon of Oushuu from Sengoku Basara. It's especially significant since he's referred to mostly by (and is infamous through) this name.
The Dovahkiin, who's title in Dragon litterally means Dragonborn.
Draco, a lawmaker from ancient Greece, from whom we get the term "draconian" as in "draconian penalties", meaning extremely harsh penalties. His name is similar enough to the Greek word for dragon, and so little is known about the man himself, that it's up for debate whether this is a coincidence, or whether Draco is an assumed name chosen to invoke this trope.
Vlad Dracul and his son Vlad Dracula of Wallachia (the bynames meaning "dragon" and "the dragon's son" respectively), who were certainly apt to invoke this trope in their lifetime. The name, however, has a relatively harmless origin story, as it became the elder Vlad's nickname when he joined the the Order of the Dragon, a late-medieval chivalric order.
Billy Drago is the stage name of a character actor who generally plays Smug Snake variants. Coincidentally, it's his mother's real surname.
Psychonauts, where Eagle is one of the four animal-themed luchadores running around in the head of Edgar Teglee, with Tiger, Cobra, and Dragon making up the rest. His catchphrase: Ca-caw!.
One Piece: Donquixote Doflamingo, a nihilistic pirate and puppet-master who slices people into pieces. He dresses in a pink, feathery coat and dabbles in slave trade, and abandons it because it's become passe (the slave trade, not the coat).
CJ's Secret Service codename on The West Wing is flamingo. She does not appreciate this.
Fox (Vixen, Reynard, etc.)
Variations of "Reynard" — the original trickster-fox from the medieval stories — include, but are not limited to, Renard, Reinhardt, Reineke; possibly even Renfield. If somebody in your group has a variation of that last name, avoid him. He's The Mole.
Film
In the Rush Hour sequels, not one but two villains have names that translate to "Fox" in that character's native language: Hu Li, from 2, and Inspector Renard from 3.
After The Fox, starring Peter Sellers as the criminal Master of Disguise "The Fox". Of course, this is a subversion, played for laughs.
The otherwise anonymous assassin, from 1973's The Day of the Jackal (an adaptation of the Frederick Forsyth novel), and 1997's remake of the movie, The Jackal.
Goku from Dragon Ball. In the first series, he has a tail, the cloud that transports him around, and his magic staff, not to mention adapted forms of many of the companions.
The title character from the Saiyuki series, a Bishounen-looking fellow restrained by the crown from the original stories, who fights with a staff.
The Monkey D. family of One Piece, which includes main character Monkey D. Luffy, his father revolutionary leader Monkey D. Dragon, and his fearsome Marine grandfather Vice-Admiral Monkey D. Garp.
The Baboon Warrior is a post-human 'tagonist (pro-? an-? it's never quite clear) from Shiva3000. He kills malfunctioning Hindu gods.
One of the lead characters in the oft-retold Journey to the West, Sun Wukong (or Son Goku).
Mustelids (weasels, skunks, badgers, and wolverines)
They may not be particularly dangerous on the surface, but they will be the sort of person who holds a grudge and will not let go of it.
Anime and Manga
Itachi from Naruto, whose name literally means "Weasel".
Years ago there was a comic series starring one Norbert Sikes, who put on a costume and fought crime in the streets as... the Badger. Yeah, he was nuts. It was a great book, though.
The Baltimore Ravens of the NFL, named for Edgar Allan Poe's poem The Raven. Definitely run, rather than try to get into an altercation with one of them in a nightclub.
Hank Scorpio, Homer's 'Bond villain'-esque boss on The Simpsons.
Scorponok of Transformers: Beast Wars was an exception. Other Transformers with the name aren't, though. And given the main theme, often were likely to have a form that involves a stinger hanging over their body.
A bird that impales insects or lizards onto sharp branches to feed on them. In short, the animal gets shish-kabobed.
Literature
The Hyperion series by Dan Simmons features a Nigh Invulnerable, time-traveling robot assassin known as The Shrike, who is definitely not someone you want to mess with, primarily because it will live up to its name.
Shrike the Stalker in the UK release of Mortal Engines (Grike in the US).
Warhammer 40,000: Captain Shrike of the aforementioned Raven Guard, who likes to pop up out of nowhere with his jet pack and impale people with his impossibly sharp weapon.
Orochimaru of Naruto fame. In Japanese, his name is usually written as 大蛇丸; the middle character 「蛇」 means "snake." Additionally, the Orochi (written as 大蛇) is itself an evil snake from Japanese mythology.
One Piece: Boa Hancock, the "Snake Princess". Also Nefertari Cobra, King of Alabasta.
William Makepeace Thackeray had a lovable traitor family named the Crawleys, and Anthony Trollope, who was heavily influenced by him gave the last name to a noble character.
It's probably worth noting Good Omens has Noble Demon Crowley originally named "Crawly" (he was the serpent in the Garden of Eden), and whose present name is an allusion to famous Satanist Alastair Crowley. (The demon's first name however, subverting this, is Anthony.)
Harry Potter — Slytherin House (whose emblem is a snake, and whose name sounds like 'slithery') and its founder Salazar Slytherin. In-universe, "Slytherin alumnus" is almost a synonym of "dark wizard".
Much like Fox, it's a trickster's name.
Anime and Manga
Onigumo from InuYasha, whose name is composed of "oni" (a troll or ogre) and "kumo" (spider). And if Kikyo had just run away from him really fast, the whole series could have been averted.
Pani Poni Dash!: Tsurugi Inugami in addition to Tsurugi, he is also Inugami — not just an animal, it is a Japanese god.
Aisaka Taiga (yes, it's pronounced pretty much the way it sounds) from Toradora. For bonus points, in addition to the Spanish meaning of the title, "Tora" means "tiger".
Averted with Harry Potter's Remus Lupin, even though he is a werewolf. Fenrir Greyback on the other hand is quite the villain (Fenrir is the giant demonic wolf from Norse Mythology).
Arkadiy Volkov, Russian chief vampire from the Midnight World. Lampshaded in the chapter La scorta: Count Saint-German's assistant juxtaposes him and the Japanese chief vampire as "White Wolf and Little Black Riding Hood".
Adolf Hitler seemed to have had an affinity of some sort for wolves. His first name derives from Athalwolf, Old High German for "noble wolf", and for this reason "Wolf" became his childhood nickname. He later used it as a pseudonym for himself in the 1920s, ostensibly for security reasons. Three of his military headquarters were named Wolfsschanze ("wolf's lair"), Wolfsschlucht ("wolf's chasm"), and Werwolf ("werewolf").
From Naruto is Hoshigaki Kisame (Kisame means demon shark) and his sword Samehada (sharkskin). It's also very literally a Meaningful Name, since Kisame looks like a shark, uses shark-based attacks and can fuse with Samehada in a shark hybrid.
Alligator Nichol from Jackals is not to be trifled with.