Billy was the volunteer that helped Dr. Alan Grant and Ellie Sattler at their dig site in Snakewater, Montana. He mainly helped with computers and was optimistic about how "Soon we won't even have to dig anymore".
In Jurassic Park III, Alan Grant's assistant at the Fort Peck Lake dig site is Billy Brennan. It is possible that these two characters are the same, although the latter is played by a different actor. However, the producers never hinted at this link and the similar name might be a coincidence.