Benny sits at #102 with 974 entries and is one of those pet names where the diminutive is doing all the work. Benjamin is a perfectly good dog name; almost no one uses it. Benny is the warmer, shorter, more affectionate cousin, and that is what owners actually want when they reach for the B-N-E sound family.
The diminutive register
Pet naming runs heavily on diminutives. Buddy, Bobby, Charlie, Tommy, Sammy. The -y ending performs a specific function: it tells you the relationship, not just the name. A dog named Benjamin is being addressed formally; a dog named Benny is being addressed as family. Owners pick Benny for the same reason they pick Buddy — they want the name to do affectionate work in every utterance.
One counter-reading: Benny lands fairly often on dachshunds and small terriers, which is a tighter breed cluster than the diminutive register would predict. The Italian-American texture of the name (Benny from Goodfellas, Benny from various Brooklyn-coded contexts) gives it a slightly streetwise edge that matches scrappy small dogs better than fluffy ones.
The sound is solid
Two clean syllables with the stress on the front (BEN-ee), opening on a hard B and resolving through a clear N. The structure rivals Luna for recall efficiency, which is part of why diminutives in -y dominate the male pet-name top 200.
The human Benny is rarer than Benjamin on SSA charts, but the parallel formal name is climbing fast. The Benjamin baby name page shows the trajectory.