Click on it, and type the name for your dog. Use an anvil to rename it.
Left click the dog with the name tag to name it. Naming a dog Dinnerbone will make it upside down. Right click on the anvil and place your name tag. Once you have renamed your name tag, take it out of the anvil and right click on your dog to name it. Don't worry! Name your dog(s). This … Above the three slots found in the anvil GUI, you'll see a bar that contains the item's name in it.

You will need to get a name tag, which is only found in dungeon, temple, and woodland mansion chests.