Cats, they have names that a normal house cat has. (Like Petal)

Humans, they tend to have normal names.

Sirens, tend to have names that can sound nice when sung and can be known about in the water.

Mermaids, tend to have names based on things in the water.

Angels, have basically any name you can think of.

Demons, same as angels.

Fairies, names vary based on the type of fairy.

Gods, they tend to have ancient names. You can not be the god of something that already has a god.

Dragons, they tend to have unique names that are similar to warrior cats names (like Moondust).

Centaur, they tend to have human like names or names based on there talents.

Giants, they tend to have names based on things high up.

I can't remember the rest of these things names right now. So suggest any more if you think of any.