I believe all dog training must start with leadership skills. It is the core of all behavior problems. The President of the United States is the ultimate authority figure for humans but that doesn't mean that they understand dog psychology. First, leadership skills, second, teach the new puppy to respond to their name, and teach the focus command.

I'd continue obedience training cues including sit, down, and stay. I believe the recall "come" command is the most important command to teach. When their dog can focus and sit on command, they should begin teaching the "running game." This is a simple game that entices the dog to follow you while you are backing up with a treat held close to you.

If behavior problems start to arise, then barking would be at the top. Can you imagine what an annoying bark must sound like in the White House?

A trained dog is a happy dog, whether you live in poverty, middle class neighborhoods or the White House. The dog doesn't know the difference.

As this prominent pup will be an ambassador for his species and his breed, it goes without saying training this dog to remain seated even after being introduced would reflect positively on good manners! Allowing dignitaries to pet or give direct eye contact without the dog moving away or showing exuberance or fear would be encouraged.

Socialization may include exposure to live music, for example brass bands, and loud engine noises such as helicopters or car engines.

Not accepting tidbits or food stealing would be another behavior to train. Remaining at his owner’s side off-leash would allow this pup to do his job and be attentive to hand signals or voice commands. Stay, down, and other basic good manner behaviors would aid in promoting the canine as the fine companion pet he is!

The new White House pup should know the basic commands that benefit all dogs (and their people). These are "Sit," and "Stay," and "Down." But better manners are expected from the First Dog.
The command "Off" will be needed to get the puppy off the furniture. It's not great to have dog hair on the chair that the President or the First Lady may soon occupy. One alternative is for them to always wear clothes with a tweed pattern.
"Leave it" will come in handy when a secret service agent's ear phone falls to the ground or when Malia or Sasha drops a Hershey bar on the floor. The pup may like the taste going down but not so much when the veterinarian is getting it to come back up.
Every dog should respond to the command of "Back" but none more than a frisky pup anticipating the opening of the door to the open spaces beyond. It may be magical to live in The White House but, for dogs, the greater privilege is to live in "The Land of the Free."