At the start of the game, two stray dogs will appear on your farm. Takakura allows you to pick one of them to keep as a pet, and takes the other one to the city to find it an owner. You get your choice of the pointy-eared dog, or the floppy-eared dog. You're able to name it using up to seven characters.
Feeding and Interaction
You do not have to feed or even interact with the dog if you don't wish to, but, if you feed it and hold it regularly, eventually it'll like you enough to give you the option to be trained. Feed your dog by putting edible items it in the dog's dish. After a bit of training, it will chase away intruders like Murrey and Daryl.
There is a rumor that, later on in the game, you can get an additional dog; the Chihuahua you see around Carter's Dig Site. Once you become good friends with him and find all of the special tablets at the dig site, he will give you the dog.