A castrated female dog is called a spayed bitch
You can't castrate a female goose. They have no testicles. A female goose is called a hen
a stud
A non castrated male cat is called a tom
A castrated dog is still called a dog. If it was a rescue dog it would be considered as being neutered.
Only non-castrated male goats are called billy.
A castrated young horse is called a gelding.
Bison generally are not castrated..
A castrated poultry is called a pullet.
When castrated he will be called a steer no matter how young.
There are many kinds of castrated domestic animals. Donkey's, geldings, and stallions are a few of the castrated domestic animals.
All male dogs are referred to as "dogs", and a castrated one can be called a "neutered dog". Female dogs, on the other hand, are referred to as "bitches". It may sound offensive, but in reality most reputable kennel clubs, breeders and dog books use this word without embarrassment. It is fine as long as you're only using it to refer to a female dog.
only non castrated male goats are called Billy Goats
Castration involves removing the testicles, since women have none to begin with a woman cannot be castrated.
A castrated male cat is usually just called a "neutered" or "fixed" male.