It's called the "teddy bear dog." Half shih-tzu and half bichon frise. In Canada we refer to the Shih-Tzu and Bichon Frise cross as Mollydogs instead of teddy bear dogs. I have two of them and they are wonderful.
The temperament and personality-traits of the Schnoodle reflect its Schnauzer and Poodle heritage. Schnauzers are naturally affectionate, protective, intelligent and strong-willed whilst the Poodle is clever, active, and excels in obedience training.