Brian Kagan is a character (played by Malachi Pearson) who appears in season three of Full House, and is one of Stephanie's friends who lives in San Francisco. He is also apparently friends with Laurie and Harry Takayama.
He first appears in "Nerd for a Day", when Stephanie invites him, Laurie, and Harry over to see Walter Berman in the same place. They instantly make fun of her when Walter says he and Stephanie are in love.
His second appearance is in "Misadventures in Babysitting". D.J. is hired to babysit Brian while his parents are away. However, despite D.J.'s honesty towards him and her wanting to be friends with him, Brian causes trouble and chooses to make a mess in the house, as well as tossing a vase into the air and then hoping it hits the floor and smashes so he can pin the blame on D.J. (who actually catches the vase before it can hit the floor and smash); even going so far as to steal her purse in the process and bribe her into giving up half her pay to be his friend. But the tables turn on Brian when D.J.'s friend Kimmy makes an entrance, and it is immediately shown he has a strong dislike for her after she threatens to kiss him if he doesn't drop D.J.'s purse, at which point he has no choice but to do so. Later, when he uses his water gun in a last-ditch effort to thwart off his enemies, his head gets stuck in the railing, and Danny has to come over and free him.
He has a baby brother named Tony, whom Danny, Jesse, and Joey babysit at the Tanner house in the aptly-named "Three Men and Another Baby", where Michelle's jealousy of Tony doesn't sit well with Jesse or Becky.