Two of my favorites are Robin Fox and Lionel Tiger, anthropologists who wrote The Imperial Animal, and who have four animal names between them.
Bird names that haven’t been mentioned yet are Wren, Stork, Sparrow, Raven, Kite, Heron, Bunting, Parrot(t), and Gannet(t).
It should be mentioned that some of the names offered are not actually animal names, but are only coincidentally the same. For example, “Shepherd” is certainly derived from the human profession, and not from the name of the dog.
More bird names: Brent (a kind of goose), Mallard, Teal, Harrier, Hobby (a kind of falcon), Crake, Snipe, Woodcock, Gull, Rook, Lark, Starling, Bullfinch, and Nightingale.
One of our sons had a teacher named Mr. Moose. If he’d had me for a student he would have gotten sick of being asked when ping pong balls were going to drop.
Terminology changes over time. Horse, Ox, and Deer are rare surnames, but long ago when family names were being handed out, Steed, Bullock, Hart, and Roe were probably more common terms, and they’re all pretty common names.
And there may have been many more animal surnames in the past. The Galton-Watson process was discovered in the 1870s. It has more applications than the extinction of surnames and families, but that was the original line of inquiry. Until the explanation of the process, it was sometimes assumed that rich, famous, titled, powerful, and respected people somehow had lower fertility than ordinary folk, because so many of the rich and famous families eventually died off without male heirs. In fact it’s a random process that affects all families; nobody seems to take much notice when it happens to poor families. By chance, as long as no new surnames are coined, a proportion of existing surnames will disappear every generation. In theory, if the process is allowed to continue for enough generations, all surnames except one will eventually go extinct. This process has been used to explain why the countries that have used surnames the longest, like Korea and China, have relatively few surnames.
In my youth, Australian politics had a twofer - Prime Minister Bob Hawke and his opposite number, opposition leader Andrew Peacock.
Australia also has a small handful of families surnamed Bilby, which I find rather interesting, as I’m not sure by what means New World animals would get on to the surname roster. No kangaroos, koalas or platypuses though, as far as I can tell.