Depends on the type of animals... @JJosaur's suggestion of "hunting lodge" is fine if the animals are your basic deer, fox, coyote, bear, pheasant, bobcat, etc., and your fabrics are leather and flannel check.
Skeletal remains of the heads of indigenous American fauna in a room with a bright palette, slip-covered furniture, rustic tables, (preferably fashioned from reclaimed wood) and Native American and Mexican details and accessories (throw in a cactus, or two) is "Southwestern Shabby-Chic".
Keep the skulls and cacti, change the palette to white and pale pastels, add a white leather sectional, a sheepskin rug, a large landscape painting with a "Marlboro Man" character in the distance, crystal chandeliers and cowboy decorations - you've got "Texas Millionaire".
Take the above, ditch the painting and the cowboy decorations, place an old rocking chair by a pot-bellied stove in the corner, throw a handmade quilt over the sofa, hang a flintlock rifle over the entertainment center, a stuffed jackrabbit and maybe a banjo... voila! : "Beverly Hillbillies".
If you've got lions and tigers and various heads with exotic tusks and horns, and you make use of palm trees and rattan furniture, the style is called: "Safari".
If you have exotic animals and plants with ornate Victorian furnishings in a dark palette, you've got your basic,"19th Century English Gentleman's Drawing Room."
If you mix Edwardian furniture, African and Asian animal corpses, knick-knacks from India and Chinoiserie - you'll have "British Importer".