the reason all domestic dogs are canis familiaris is because they’re all the same species. They can all have non-sterile babies with each other, which is the most commonly accepted definition of a species. A domesticated coyote would still be its own species and get its own scientific name because it would not be able to breed with dogs, at the very least without having a sterile baby.
I hate to well actually you but coyote can breed with dogs and the offspring are known to be fertile for at least 4 generations.
https://en.m.wikipedia.org/wiki/Coydog
The same is true for wolf-dogs.
There are increased chances for complications so i guess fertility is lower but that is only verified to be true with wild parents specimen.
Domesticated coyote would likely be bred based on properties like ability to coexist with dogs so over time the species would merge more and more, complications would smooth out.
I believe we have a similar history with the neanderthaler.
