Tyrann Mathieu, a football safety on the NO Saints, has had the nickname the Honey Badger since college.
Lora, at that, is a snake found in South America, so — how about Lora Lee Michel, from the Golden Age of Hollywood? She was — well, yes, she was the one playing the little-kid version of Jill Young so Terry Moore can play the all-grown-up version in MIGHTY JOE YOUNG; but, to bring this back around, she was also the one playing the little-kid version of Virginia Cunningham so Olivia de Havilland can play the all-grown-up version in THE SNAKE PIT.
“Cubby” Broccoli
Similarly, Peter Coyote (again)
Thanks to the Katmai bears coverage, I’ve learned that a coy means “Cub of the Year.” I dunno, ask my wife.
Also qualifies for the “Famous people with plant names” thread. Not that I’m going to start that thread or want anyone else to do so.
Such a wit, you are. 
I bow to the master!
Such deference! You’d think I was Elvira, Mistress of the Dark, or something!
Governor of New York, U.S. Senator and Secretary of State under Grant. You’ve seen his name if you’ve ever crossed the Hudson river on I84.
Orson Bean
Orson = French for “bear cub”
Bean = Bean
There was a Fish in the OP. And I did say we need only one of each animal. So one Fish good; two Fish bad. (Red Fish, blue Fish optional.)
Only English animal names. So he only gets into the plant thread which we aren’t doing.
You need to be the one who tells him that. He scares me. 
Another entry for the list that is and the list that never was: Oscar winner Emerald Fennell, writer/director/producer of SALTBURN and PROMISING YOUNG WOMAN — whom you maybe recognize as Camilla Parker Bowles, from THE CROWN.
If anyone here is a fan of RESIDENT ALIEN, then you can back me up on the fact that Jenna Lamia is terrific at what she does on the show…
And, for that matter: Annette Bening did a terrific job of portraying record-breaking swimmer Diana Nyad.
“Winston Churchill’s chief military assistant during the Second World War” — who then went on to serve as the first secretary general of NATO — was Pug Ismay.
Wolfgang Wolf, a one time manager of Wolfsburg football team
Bear Grylls’ given name is actually Edward. So he’s Teddy Bear Grylls.
Does that count?
j
Edward Bear is the code name of Winnie the Pooh.