A lot of the food shown is actually incredibly unhealthy and dangerous for a real dog to eat.
Winston appears to be a Boston Terrier, known for being an intelligent dog breed with expressive features and playful disposition.
The second time Winston eats dog food, you see a side view of his bowl that says 'Wins,' and then when he is eating bacon and eggs, his bowl shows a view from the opposite side that says 'ston.' This is the first indicator that Winston is the dog's name.