Redbeard was the nickname of a childhood companion of Sherlock Holmes, primarily depicted as a dog (Irish Setter) with which Sherlock shared a great attachment. Redbeard was so named because of Sherlock's longing to be a pirate during his childhood. In the episode "The Final Problem" it is revealed that the Holmes family had never in fact owned a dog. Redbeard had been a fiction of the young Sherlock, invented to repress the memory of his childhood best friend Victor Trevor whom Sherlock would often play pirates with (using the pirate names "Redbeard" and "Yellowbeard" respectively). Sherlock, traumatised by Trevor's murder at the hands of his 5 year old sister Eurus Holmes, chose to remember his best friend instead as an Irish Redsetter.
Mycroft Holmes has a note in his diary that reads "Redbeard".