Matthew is a Biblical Hebrew name — from Mattityahu, meaning "gift of God" — that became one of the most consistently used English given names from the medieval period through the present. As a pet name at rank 2651, it's almost certainly a human-name transfer: an owner who named their dog after someone they love, after themselves, or simply chose a familiar human name without much ceremony.
The Human-Name-as-Pet-Name Pattern
Matthew at this rank in pet licensing data represents the substantial category of dogs named with ordinary human first names — particularly names that were common in the 1980s and 1990s, when many current dog owners were growing up. Matthew was a top-10 baby name in the US from the 1970s through the 1990s. Naming a dog Matthew is an act of comfortable familiarity. Compare Michael, Christopher, and Steven for the same era and register.
The Apostle and the Pop-Culture Layer
Matthew the Apostle gives the name its Biblical depth; Matthew McConaughey, Matthew Perry, and Matthew Broderick represent its pop-culture dimension. The human name Matthew has been in continuous use for over a thousand years in English-speaking contexts. On a dog, it reads as companionably human.
The Counter-Reading: Very Ordinary
Matthew on a dog generates almost no reaction — which is either a relief or a missed opportunity depending on what the owner wanted from the naming exercise. Golden Retrievers and Labradors suit its uncomplicated warmth perfectly.