Michelle is the French feminine form of Michael, from Hebrew meaning "who is like God?" It peaked as an American human name in the 1970s. On a pet, it occupies the retro-human-name crossover space: a fully functioning person's name with enough generational distance that it reads as affectionate rather than simply current.
The 1970s Name Aesthetic
Michelle sits in the same generational register as Linda and Donna: human names that peaked in the postwar decades and now carry warm nostalgia. Owners who choose Michelle for a pet are usually making an affectionate nod to someone specific.
The Beatles and Michelle Obama
"Michelle" (1965) by The Beatles gave the name its most celebrated moment. Michelle Obama has since given it a different contemporary resonance: accomplished, composed, public. Both associations work in the pet's favor.
The Counter-Reading: Fully a Human Name
Michelle is so thoroughly a human name that calling it at a dog park produces a double-take. The human name crossover is essentially complete; there's no pet-specific layer here at all, which is precisely its appeal to owners who want their pet named like a person.