The last name (or family name) of the children in “A Series of Unfortunate Events” is Boudelaire. The children are, from oldest to youngest, Violet, Klaus, and Sunny. The kids, as the title suggests, go through a series of quite unfortunate events over the course of thirteen chapter books. SPOILER ALERT. Stop reading if you haven’t at least read the first book.
The three kids are orphaned early on, and there’s a recurring image of an eye, because in the first book, they are sent to live with their Uncle Olaf - a con man disguised as an actor who wants the fortune. He follows them the rest of the series, and the eye image comes in because he has tattooed an eye on his ankle.