Register them with *whom*?
They’re not a breed, as we term a breed.
There’s no “registry” unless you count the “pit bull” registry which is only for tracking “lines”.
Most any dog (even mutts) can be enrolled in AKA’s “Canine Partners” if not registerable — perhaps I should have said “enrolled or registered”. The point is, the majority of dogs are not reliably “recorded” in any way, and registries are likely not an accurate guide to actual popularity / population.