This 'American primative' of a dog is a real favourite from my collection of paintings.
This is what's written (in very faded ink) on the back of the split wooden panel.
'Mrs Ellen McAulay. Fitts Corner. Wyoming. 13th November 1842'.
No name for the dog, or why he was painted. I quite expect that originally the wooden panels were part of a cupboard door. On several occasions when I've had dogs in the house, they've put their front paws up against the wall (below the painting) and barked. I think the artist would have been highly amused.