Chachi appears 64 times at rank 1605 on male pets. The name is almost entirely a Happy Days artifact: Chachi Arcola, played by Scott Baio, was a beloved character from the 1970s-80s sitcom. Owners choosing it are either nostalgic for that era of television or received the name from an older family member who was.
The Happy Days Pipeline
Chachi Arcola was Fonzie's younger cousin: cool-aspiring, lovably overconfident, eventually the lead of the spin-off Joanie Loves Chachi. The character's name was based on an Italian-American dialect term and it carries the warmth and slight corniness of 1970s television throughout. On a dog, Chachi signals a specific generational nostalgia most common in owners over 50 or in households where that television era is held warmly.
Sound and Breed Fit
CHA-chee is two syllables with a bouncy, doubled sound that suits a lively, sociable dog. The name fits breeds with outgoing, slightly show-off personalities: Chihuahuas who think they're much larger than they are, or Jack Russell Terriers who have already decided they run the household. The human comparison is at /names/chachi.
The Counter-Reading
Chachi's pop-culture origin is specific enough that it dates the owner's reference points clearly. Younger owners who use it are usually doing so ironically or through family transmission. The name is warm and doesn't take itself seriously: qualities that work well for a certain kind of dog.