Who is this man in Black Adder?

In the pilot for the series, the pet was originally a dog in the cage:

According to The True History of the Blackadder: The Unadulterated Tale of the Creation of a Comedy Legend (p. 107), the pilot was remade into the episode you cite. "Perhaps as a response to The Young Ones' surreal dimensions," the jokes were more outlandish in the series than the pilot, "the dog which Edmund kept in a cage in the pilot had now become his pet dwarf, for instance." You can watch the pilot in three parts on YouTube. Edmund in the pilot is more like the Edmund of the later Blackadder series rather than the doltish fellow we see in the first season.