In The Lives of Christopher Chant, Oneir was one of Christopher Chant's two best friends at Penge School - the other was Fenning - but we never learn his first name, because it's one of those traditional school-story schools where people address even their friends by surname. He is described as "restfully ordinary". His father was a businessman, and Oneir was expected to follow in the family business when he finished school. He had some magical talent, and did Christopher's magic schoolwork in exchange for Christopher doing his algebra. He also helped Christopher pick out books to give the Living Asheth (although Christopher of course didn't tell him exactly who they're for), as he has an elder sister with whose tastes he is familiar. The fact that Christopher is a nine-lifed enchanter was discovered after Oneir accidentally belted him in the head with a cricket bat.
In "Carol Oneir's Hundredth Dream", Oneir is the father of best-selling dreamer [Carol Oneir]?, and takes her to see his old school friend - now the Chrestomanci - when she develops dreamer's block. As an adult he is a level-headed man whose response to a crisis is to go fishing until the fuss dies down. (Although, in fact, on both occasions in the story when he goes fishing, it turns out to be a cover for some other activity.)