What do you call an embalmed animal? You sometimes see them at museum and they look real and they don't rot somehow. Do they have a name? I suppose they do have a name, but I have no idea what it might be.
I think the term you might be looking for is 'taxidermy mounts'.
Taxidermy is the preserving of an animal's body for the purpose of being put on display. A person who creates these displays is called a 'taxidermist'. The end result is called a 'taxidermy mount' or just simply 'taxidermy'. There are different methods used in taxidermy such as overlaying the animal's skin over a frame of wood and wire and then stuffing it with cotton, creating replicas with resin or fiber glass, or freeze drying the whole animal and removing its organs.
Preserving chemicals are sometimes applied to the skin used, or the skin is tanned, which is why they do not rot over time.