Bugs Bunny — Looney Tunes' wisecracking, carrot-chomping antihero who debuted in 1940 and never stopped being culturally relevant — is the obvious and entirely correct reference here. A pet named Bugs is almost certainly a Looney Tunes tribute, and it works best on an animal who shares Bugs's core qualities: unflappable, clever, slightly smug, always winning.
The Looney Tunes Legacy
Bugs Bunny has been continuously in production in some form for over 80 years — Space Jam in 1996, Looney Tunes: Back in Action in 2003, The Bugs Bunny Show revivals. The character is genuinely multigenerational. Actual rabbits named Bugs are an obvious and affectionate choice; so are dogs and cats with that "what's up, doc?" energy of studied nonchalance. Holland Lop rabbits are the purest expression.
One-Syllable Practicality
Bugs is short, punchy, and impossible to accidentally shorten further. It works for training recall as well as any monosyllabic name. Browse classic cartoon-inspired options at pet names.
The Counter-Reading: Insect Ambiguity
"My cat is named Bugs" does occasionally produce a confused pause from people who don't immediately land on Looney Tunes. A quick "like Bugs Bunny" resolves it instantly — and usually generates a smile.