I've only done characters with extensive backstories or significant impacts on the plot, as, if I did all the Enchanted Forest characters, I'd be here forever. I didn't do Henry, because his daemon wouldn't have settled yet, I don't think. But I have named her 'Viera' (Slovak word for 'faith'). And I didn't do Ingrid/the Snow Queen because I didn't feel we knew enough about her life yet.
I have a vague headcanon that someone who has had their heart removed can't communicate with their daemon as clearly, and that the use of Dark Magic also corrupts your ability to communicate with your daemon.
Jaeger (German, meaning 'hunter')
Emma spent most of her life on her own, being moved from place to place, looking for a home and a family. I thought Jaeger might settle into something comforting and loyal to cheer her up and snuggle with her when she felt alone. Also, a form that might be appealing to a prospective family. Beagles are amazing scenthounds, and Emma worked as a bounty hunter, and the last words she heard from her parents were 'find us', so I thought settling into something good at finding made sense.
Phoebus (Greek, meaning 'bright, pure')
Most of Snow's troubles didn't begin until after Phoebus would have settled, and her childhood was a relatively happy one, and she was a friendly, cheerful child, and despite her troubles, she remains a happy, optimistic, loving person. Lovebirds are very cheerful and playful, and love to explore and stick their noses into things. They also have a reputation as being mated for life, and Snow and Charming's motto is 'I will always find you'. Plus, they are small and quick, so make good thieves, as Snow was for a while.
Comina (form of 'Jacob', meaning 'supplanter'), Agaway (from Agaue, meaning 'noble')
David started out life as a shepherd before he was called on to replace his twin after his death and had to take a sudden level in badassery. So, I didn't want anything too stereotypically princely for him. Albatrosses travel huge distances to return to their homes and mate, and they mate for life. They also go through elaborate courtship dances and take a while to find the right partner, which suits Snow and Charming as well. In universe, my canon is that David's daemon, Comina, was forced to take on the name of James's daemon, Agaway, once he was forced to become the Prince. He calls her Aggie, now. King George concocted a story of James having a massive change of heart due to his encounter with the dragon and upcoming responsibilities as a husband to explain why James' daemon was now a different animal.
Perseus (Greek, meaning 'to destroy')
A lot of Regina's troubles didn't start until her teens, but she still had a lot of expectations placed on her by Cora. Regina states what she really wants is freedom, not power, so I thought Perseus might settle as something that could fly. Falcons are noted as symbols of royalty, which would be amenable to Cora, but they're also regarded as creatures who are single-minded and hot in pursuit of a goal, which certainly describes Regina's determination to have revenge on Snow White.
Ferdika (from Feardorcha, meaning 'dark man')
A lop-eared rabbit
Before Rumpel became the Dark One, his main characteristic was that he was a coward, so I didn't want anything too terrifying, despite the power that the Dark One possesses. Rabbits are quiet, and bolt and hide instead of putting up a fight. Also, similarly to Emma, Rumpel was a lonely child who probably wanted something soft to snuggle with. Rabbits are also known as trickster animals in some folklore, which matched Rumpel's love of making deals that don't turn out to be what they seemed at the start.
Cercatrix (from Cercatrice, meaning 'seeker')
I imagine Trix settled after landing in the Land Without Magic, as being abandoned by your father in an unknown land is a good time to grown-up. Since Bae had to forage and steal and fend for himself, I thought a scavenger animal would suit the job. Neal ultimately ended up as a thief, and raccoon have a folkloric reputation for being thieves.
Killian Jones/Captain Hook
Pelagiya (Russian, meaning 'the sea')
a roseate tern
Terns are seabirds and Hook was sailor in Some Majesty's Navy before he became a pirate, and his love his ship and sailing runs pretty deep (so much that giving up the Jolly Roger is one his big acts of sacrifice). Roseate terns spend the most time at sea of the tern family, and they also, unusually for terns, exhibit parasitic feeding, which means they steal food from other animals. Like a pirate.
Kirja (the Finnish word for 'book')
What Belle truly wants is to be a hero like the ones in the books she reads, and like her mother. Quokkas are small little rodents who are very curious and forthright, and love to come up and meet anyone who is in their habitat. I liked the idea of having a small furry creature, to represent the nerdy, bookworm side, but one who's rather bold and daring, to represent Belle's desire for adventure.
Fallyn (From Faolan, meaning 'little wolf')
A corsac fox
Graham was literally raised by wolves (of the 'were' kind) but at the same time is the only member of his family who isn't capable of shape-shifting into a wolf, so is on the outside a little, and ultimately leaves the pack to strike out on his own. So I settled on something in the canid family, and that looked like a wolf, but wasn't one, to show that outsider, independent side. Corsacs are exceptional hunters, and capable of climbing trees. They are nomadic and will work both alone or with a pack, unusual for foxes, which normally live alone.
Ivarra (from Ivar, meaning 'yew bow warrior')
A pine marten
To me, pine martens are the swashbucklers of the animal word. They're very agile and jump along branches and trees and look like badass little adventurers, with sort of a dashing, rogueish air. I also wanted something that lived in the woods, as Robin lives in Sherwood Forest, and something playful and cuddly, as he is a family man who loves his son.
Taimi (Finnish, meaning 'little tree')
I don't think Pinocchio would have had a daemon when he was still a puppet; I think one of the boons of becoming a 'real boy' would be to get one, so Taimi didn't appear until the Blue Fairy transformed him. He ended up in the Land Without Magic as a very young boy, and abandoned Emma to pursue his own pleasure, despite promising to take care of her, something he later came to regret. I thought Taimi might settle as a woodpecker as a sign of a bit of self-loathing, and a warning that if he kept running from his duties, he would turn back to wood. Taimi went back to being unsettled when August was turned back to being a boy.
Astra (Greek, meaning 'star')
Malcolm was originally a trickster and conman, and coyotes represent tricksters in many legends. I think Astra would have gone back to shapeshifting again after Malcolm regained his youth, as part of the idea of 'never growing up'.
Sidney Glass/The Magic Mirror/The Genie
Abhilasha (Arabic, meaning 'wish')
a glasswinged butterly
Like August, I don't think The Genie would have had a daemon until he was released from the lamp by King Leopold. I don't think Abhilasha would have settled right away, despite his being a grown-up, so I don't think she would have chosen a form by the time he wished himself into the mirror. But in Storybrooke, he, to appear like a human adult, would need a settled daemon, and I like to think that Regina had a bit of a laugh making her glasswinged. But since what he wanted most was freedom, a butterfly seemed to fit that, as well as his status as a person who writes the newspaper and digs up dirt, so who flits about a lot.
Cora/The Queen of Hearts
Pancratius (Greek, meaning 'all-powerful')
What Cora has always wanted was power and to be royal, and when her pride is hurt, she sets out on a life-long mission to better herself. Peacocks have a reputation for being vain, and for being royal, as well as in mythology being immortal, as their flesh was believed never to decay. And it was very hard to kill Cora.
Narkiso (from Narkissos, meaning 'sleep')
Aurora didn't get a whole lot of character development, but from what we did learn, she's a bit princessy, but capable of doing what needs to be done when asked for it. Ermines are a symbol of purity as they were believed to rather be captured than get their white coats soiled by dirt. I thought that suited a bit of a spoiled princess who isn't dressed for adventure. However, ermines are part of the weasel family, which means they will go hardcore on your ass if threatened. And Aurora will seek revenge if you cross her.
Yongshi (Chinese word for 'hero')
Mulan was called very early in her life to serve as a great warrior, and the pangolin's scales reminded me of a suit of armour. They also use the sharp side of their tails like a sword when they attack. They are known in Chinese by a name meaning 'that which digs through the mountain' which seemed like it could be a metaphor for a person who does great, unlikely things, and Mulan carves her own path.
Zelena/Wicked Witch of the West
Viridis (Latin, meaning 'green')
A peron's tree frog
Zelena's defining trait is her jealousy, which turns her green as time goes on. Peron's tree frogs get green spots as they age. They are also capable of rapidly changing their skin colour on command. They make a cackling sound, and frogs are commonly associated with witches, so it seemed appropriate for Zelena, who was so desperate to learn and use her magic.
Ruby/Little Red Riding Hood
Flann (Irish, meaning 'red')
An Irish wolfhound
Ruby wouldn't have found out about her werewolf status until after Flann settled, but I thought she might instinctively know something was off about herself, and that Flann might settle into something to keep her in line. Wolfhounds were bred to hunt and follow wolves, so Flann could still keep up with her when she was in wolf form, and may be able to stop her from doing something bad, once he got the hang of the whole werewolf thing.
Sen (Czech, meaning 'dream')
Dwarves aren't born, they're hatched fully grown from eggs and spend their entire lives in the mines, so the canon I came up with is that all dwarves have canary daemons, as canaries used to be important to miners.
Archie Hopper/Jiminy Cricket
Kita (Maori word meaing 'to chirp')
I had a bit of trouble deciding what happened to Kita when Jiminy was transformed into the cricket. By doing that, he essentially became a daemon himself--acting as a guide and conscience to Gepetto and Pinocchio. I decided that Kita would have settled into a cricket to be with him and be able to communicate with him without him having to use his magic megaphone. Crickets are important to Jiminy, as his only happy childhood memory is listening to them sing, so it seemed a suitable choice for Kita, even beyond the fact that she's literally a cricket's daemon.
Fredian (from Frediano, meaning 'cold')
A snowshoe hare
The Frozen movie, unlike the other Disney movies, seems to remain canon in OUAT, so I have a little more backstory to work with than what we've seen on the show. Elsa spends most of her childhood locked in a room, afraid, so I wanted something nervous and shy for her. Snowshoe hares live in the arctic, so they can withstand cold temperatures, and they spend most of their day hiding in their burrows. Also, because of the 'conceal, don't feel' mantra, I thought something that was quiet and camouflaged (at least in the snow) suited.
Josse (French, meaning 'playful')
An Atlantic puffin
This was more of case of 'I could see Anna with a puffin' than really good reasons why she should have one. But puffins are cute and clumsy, and a bit flaily, but they mate for life, and Anna desperately wants to find her true love. They also spend a lot of time on their own at sea, and Anna spent a lot of her childhood on her own in the castle. She has some hidden badass skills, and puffins look like they could go ninja on you if required.