A statement posted on the official White House website said Sunny was born in Michigan in June 2012 and joined the first family Monday.
The Obamas' first Portuguese water dog is Bo. The Obamas favor the breed because of allergies in the family.
"Sunny is the perfect little sister for Bo -- full of energy and very affectionate -- and the first family picked her name because it fit her cheerful personality," the White House statement said.
"We suspect Sunny will follow in Bo's footsteps and keep the president company in the Oval Office, go for walks with the first family after their 6:30 family dinner and even jump up on the first lady's lap from time to time!"
The Obamas will make a donation to the Washington Humane Society in honor of their new pet, the White House said.