I am curious to find out how people go about naming the beasts that they buy and breed.

For a long time, I named my pets whatever I wanted. However, this got confusing when I had to manually go and check their lineage to avoid inbreeding, so I ended up naming them like this:

Mother's name + Father's name + Gen #

Pets that I purchased whose parents I do not own are classified as Gen 0 and do not have the Gen marker in front of their names. When I breed them their offspring is called Gen 1, and when I breed the Gen 1 with another pet the baby is Gen 2, and so on.

I've found it helpful to keep track of my beasts, especially when it comes to my cockatrice breeding project and I had a small pool of breeders and several generations of similarly named cockatrices.

I number mine so as it's easier to keep track while breeding.