I see a couple of people mentioned Shakespeare, but if you want to quote Shakespeare you should say "What's in a name? A rose by any other word would smell as sweet." If you say "by any other name" you're quoting one of his folio editor's mistakes.
There are a number of animals that have been used for these sort of metaphors that are in in some cases idioms. The oldest is derived from the Bible (changing one's skin/spots/stripes). There are a number of expressions related to pigs tracing back to the 16th century, but picking up variety in the 1900s American rural communities and recently adopted by a number of politicians. There is a famous expression related to ducks which began with the anti-communist fever in the post-war 1940s (despite a typical misleading reference from Wikopedia). Finally there are animals which the smell of indicates detecting deception or falsehood, like smelling a rat or fish.
1) “Can the Ethiopian change his skin, or the leopard his spots?”
2) "the tiger cannot change its stripes"
3) "a zebra cannot change its stripes"
sources include: The American Heritage® Idioms
1) "You can't make a silk purse from a sow's ear" (from mid 16th
2) "A hog in armour is still but a hog" (Thomas Fuller 1732)
3) "A hog in a silk waistcoat is still a hog" (Charles H. Spurgeon in
his 1887 compendium of proverbs, The Salt-Cellars)
4) "You can educate a pig but all you get is an educated pig" (I heard
this old phrase used in Texas)
5) "Never try to teach a pig to sing - it wastes your time and annoys
the pig." (Robert A. Heinlein's 1973 novel Time Enough for Love)
6) "like putting lipstick on a pig" (Washington Post 1985)
7) "put lipstick on a hog and call it a princess" (Ann Richards 1991)
8) "You can put lipstick on a hog and call it Monique, but it is still
a pig" (Ann Richards 1992)
9) "You can put lipstick on a pig but it's still a pig" (Barrack Obama
10) "Just weighing a pig doesn't fatten it" (Barrack Obama 2009, which
he said he heard in Illinois rural communities)
"when I see a bird that quacks like a duck, walks like a duck, has
feathers and webbed feet and associates with ducks—I’m certainly going
to assumer that he IS a duck." (Emil Mazey 1946)
"When someone walks like a duck, swims like a duck, and quacks like a
duck, he’s a duck." (James Carey 1948)
"When you see a bird that looks like a duck, walks like a duck, and
quacks like a duck, it’s a duck." (attributed to Walter Winchell 1951)
smell a fish/rat/fault
1) "Do you smell a fault?" (King Lear)
2) "smell a rat" (June 1851 in the County Courts Chronicle
"Two other cases the witness mentioned, in the first of which he
alleged that the judge, in reference to an insufficiency of evidence
said, 'I smell a rat; I don't believe the defendant or her witness.'"
3) "smells fishy"
sources include: knowyourphrase.com