Zachary on a dog is almost certainly a name borrowed directly from a human family member. The name was a top-20 boys' name through the 1990s, and dogs named Zachary today are predominantly owned by millennials who grew up with a Zachary in the household: a brother, a neighbor, a best friend who transferred that affection to their pet.
The Millennial Memory Bank
Zachary reached its peak popularity in the early 1990s, making it one of the defining male names of that generation. The generation now in peak pet-ownership years has a strong Zachary association baked in — whether from Saved by the Bell's Zack Morris (technically Zachary) or just from statistical probability. Dogs carrying the name today are living monuments to 1990s name culture. See also: Brandon, Tyler, and Jordan for the same cohort effect.
Formal Name, Casual Dog
Zachary is a three-syllable formal name that rarely gets used in full on a dog — in daily use, it almost always collapses to Zach or Zack. The full name on licensing paperwork suggests either a formal household or an owner who wanted the full name on record while using the short version in practice. Either way, Labs and goldens dominate this name.
The Human Name Today
The baby name Zachary has faded from its 1990s peak and now reads as a Gen-X/millennial marker rather than a current trend. On a pet, that generational placement is part of its appeal: warm, familiar, and immediately relatable.