Danger is a maximalist name chosen for ironic contrast or earnest swagger, and in either case it works. A tiny dog named Danger is funny. A large, physically imposing dog named Danger is intimidating in exactly the way the owner intends. The name announces itself before the animal does, which is either the point or a side effect the owner has fully accepted.
Owner-Type Segment
Danger belongs to the same category as Havoc, Chaos, and Menace: names chosen by owners who want their pet's name to do some personality work upfront. This tends to be male dog owners with a taste for names that land on the assertive end of the spectrum. Whether the pet actually lives up to the name is beside the point; the name creates an expectation, and that expectation generates conversation.
Sound Fit
DAYN-jer: two syllables, the first stressed with a hard d, the second resolving on a soft r. It's a strong recall name with no ambiguity. Large breeds like Rottweilers, Pit Bulls, and Cane Corsos receive it in earnest. Small dogs receive it ironically, and both applications have genuine entertainment value.
The Counter-Reading: At the Veterinary Desk
Announcing that you're checking in Danger at a veterinary reception desk produces a specific look from the staff. Most owners find this amusing. Owners who prefer not to have that interaction repeatedly might consider Ranger: same terminal sound, adjacent energy, considerably less explanation required.