Della registers 63 times at rank 1624 on female pets. It's a vintage given name, historically a diminutive of Adela or Adelaide, that's been hovering in the background of American naming culture for decades and is starting to feel genuinely fresh again. On a pet, it reads as the kind of name owners choose when they want something old but not stuffy.
The Vintage Revival Register
Della belongs with Pearl, Mabel, and Hazel: names that skipped a generation and are now being reclaimed by owners who find them charming rather than dated. The human name has a sustained presence in SSA data and is currently trending upward. See /names/della for the full trend picture.
Sound and Breed Fit
DEL-lah is two syllables, warm, and easy to say quickly. It suits medium and small female dogs with gentle temperaments: Cavalier King Charles Spaniels, Cocker Spaniels, and any cat with a dignified, slightly reserved personality.
The Counter-Reading
Della is soft enough that it can feel understated in a loud environment, but the name's appeal is precisely its quietness. Owners who choose Della are usually not trying to make a statement. They found a name they genuinely love, and that tends to be the best reason to choose any name.