It is called 'Snap Dragon' because of the opening and closing of the mouth of the flower when squeezed resembles the opening of dragon's mouth.
It is called Dog flower or Shwanmukh mainly because if the sides of the flowers are gently squeezed at the right place rhythmically, it will open "pop" and close "snap" (shut again) like the jaws of a dog.
This fun activity is very popular among the children and even grown-ups.