Own animals and monsters in Minecraft?

Is there any method in Minecraft (1.16) to add your own monsters and animals with command or data packs and resource packs? I've seen videos where people did it, but I don't know if they had to replace other animals or monsters or if they really added their own.

You can't "replace" via command block or datapack and resource pack mobs, but you can:

Own models
Textures
Sounds

insert and specify in the data pack with commands what they should do