Steven is the American spelling of Stephen — from the Greek Stephanos, meaning "crown" or "garland" — and as a male pet name, it represents exactly what it looks like: someone named their dog Steven. The crown etymology is excellent, the cultural history is rich (Saint Stephen, Steven Spielberg, Steven Tyler), and none of it is likely why this dog got the name. The dog got the name because the owner had a Steven in mind.
The Human-Name Transfer
Steven appears in pet licensing at rank 2679 alongside Matthew, Rick, and Ron as part of the substantial category of ordinary American male names given to dogs. The owner's relationship to the name is almost certainly personal: a tribute to someone loved, a name that arrived fully formed when they met the dog, or a preference that had nothing to do with pet-naming conventions. The human name Steven peaked in the 1950s–1970s; most current dog owners with a Steven were children then.
The Pop-Culture Dimension
Steven Universe, the Cartoon Network animated series (2013–2019), gave the name a new generation of fans who associate it with empathy, creativity, and emotional intelligence. A dog named Steven in a household that loved the show carries the character's warmth without requiring the name to be explained. Golden Retrievers are the Steven Universe dog without question.
The Counter-Reading: The Spelling Question
Steven vs. Stephen is a spelling distinction that matters to some people and not at all to others. On a dog, the choice is entirely the owner's — but it signals something about how precisely they think about names, which is its own kind of personality test.