Henrietta is an elaborately formal name, the feminine form of Henry via French and German, that owners apply to pets with a maximum of affection and a minimum of irony. A rabbit, a guinea pig, or a particularly dignified cat named Henrietta is a specific joy. The name carries Victorian formality that sits perfectly on small animals who absolutely do not need that level of gravitas.
The Formal Name on a Small Animal
There's a great tradition of giving tiny, fluffy, or otherwise undignified animals extremely formal names. Henrietta participates fully in this tradition. The contrast between the ceremonial weight of the name and the animal's actual behavior (eating pellets, zooming across the living room, ignoring commands) is the entire point. Small breed dogs, rabbits, guinea pigs, and opinionated cats get Henrietta most frequently. Lop rabbits and other round, soft animals with elaborate ears seem made for it.
Human-Pet Crossover
Henrietta as a human name has been cycling back toward fashionable among parents drawn to Victorian-revival naming — the same wave that's reviving names like Genevieve, Adelaide, and Josephine. That revival makes Henrietta feel less dusty and more deliberately chosen than it did a decade ago. The nickname Hettie is charming. Henri is also available and feels more modern.
The Counter-Reading: Five Syllables
Henrietta is a five-syllable name. No one is using all five syllables in daily pet interaction. You will call your animal Hettie or Henri or simply Etta. The full name appears on the license and in formal introductions. That's fine — the full name matters even when the nickname does the daily work.