I love animal nicknames (i.e. little boy named [name]Foster[/name] called [name]Fox[/name]…)
I wouldn’t feel that you could just call a child [name]Fox[/name] (or [name]Tiger[/name] or [name]Bear[/name] etc.)
I feel you would need a REAL name that is connected to the nickname
What names do you see having animal nicknames? What do you think of animal nicknames?
Subbing to see what others have to say on the subject. Personally, I’m obsessed with [name]Fox[/name] as a full name, but I know that not most people’s style 
[name]Hawthorne[/name] nn [name]Hawk[/name]
[name]Bernard[/name] nn [name]Bear[/name]
[name]Colbert[/name] nn [name]Bear[/name] (any -[name]Bert[/name] name will do)
[name]Randolph[/name] nn [name]Wolf[/name]
[name]Lauren[/name], etc nn [name]Wren[/name]
[name]Birgit[/name] nn [name]Birdie[/name]
[name]Roderick[/name] nn Rook
[name]Boris[/name] nn Boar
[name]Tigris[/name] nn [name]Tiger[/name]
[name]Lionel[/name] nn [name]Lion[/name]
I love [name]Colbert[/name] nn [name]Bear[/name]!
blade, way to go! I love [name]Bernard[/name] nn [name]Bear[/name] 
I love animal nicknames! My mom had one for each of us, although they weren’t based on our names (I was butterfly. :)). I think [name]Barrett[/name] nn [name]Bear[/name] and [name]Foster[/name] nn [name]Fox[/name] are cool, I’m not sure about others. I like @blade’s suggestion of [name]Lionel[/name] nn [name]Lion[/name], too. Or even something like [name]Leander[/name] or [name]Leonardo[/name]…
Definitely loving [name]Bernard[/name] nn [name]Bear[/name] and [name]Barrett[/name] could work too!
[name]Jebadiah[/name] nn Badger? Lol. I think this is not my strength.
I disagree! I think you can call any child any animal name without a connection to their actual name. It can be due to physical resemblance, or to personality/physical antics. 
I know many girls nicknamed Monkey for example, and their names have nothing to do with Monkey’s, or the letter M.
I was nicknamed Bumblebee/Bumble Rumble at a camp once because I wore yellow and black one day and it just stuck.
I think they can be cute.
[name]Jay[/name] works for any J name
[name]Hart[/name] could work for [name]Charles[/name], [name]Harlan[/name], [name]Harley[/name], Harlend, [name]Harold[/name], [name]Harmon[/name], [name]Harrison[/name], [name]Hartley[/name], [name]Hartman[/name], etc. (hart is a deer)
[name]Bee[/name] works for any B name really, especially [name]Beatrix[/name] and the like for girls, not as useful for boys though
[name]Fox[/name] could also work for [name]Ford[/name], [name]Forrest[/name]
[name]Drake[/name] for [name]Frederick[/name] or [name]Hendrick[/name] or [name]Roderick[/name]
[name]Finch[/name] for [name]Finley[/name], [name]Finnegan[/name], [name]Griffin[/name]
Some would only really work for younger kids like:
[name]Caleb[/name]: cub
[name]Phillip[/name]: pup
[name]Wolf[/name] works on its own! Also as a nn for [name]Wolfgang[/name].
I also like [name]Robin[/name] for a boy.