At the end of the episode, where the elder starfish found a coffee stain revealing Gary as Sluggo's son, and the rightful king of Bikini Bottom.
He is never mentioned or appeared in an episode, although he is seen during the episode on the poster. He might have died, but it is unknown why if he did because Gary seems young.
Given that the right to become King was passed to Gary, rather than Patrick, this implies that Sluggo is the older or younger brother of Herb.
His surname is likely Star, as that is his brother's surname, which also makes Star likely to be Gary's surname.
It is possible that Sluggo was adopted, given that he is a mollusc, yet both of his parents are starfish. He could have a similar story to Darwin from The Amazing World Of Gumball, from pet to brother.