This is called a self-portrait because the man on the left of the picture wearing the pale-coloured jacket, is Louis Laguerre, the artist who painted all the frescoes in the Saloon, including this one.
Next to him is a man called Dean Jones. He was chaplain to the 1st Duke, but the Duchess didn't like him very much. Can you tell that from the way Laguerre has painted him? Remember, it was the Duchess who was going to pay Louis Laguerre when he had finished the work.