Do anorexic people know that they are anorexic?
Like all mental issues, some people are aware of their condition, and others aren’t. Typically, those who have anorexia who don’t believe they have it have thoroughly divorced the way they see their body from the way it actually is; their continued fasting and working out is seen as continued progress towards their “ideal weight”, whatever that happens to be. As the answerer above me notes, some people are fully aware that they have it, but the habits they’ve accrued are difficult to break at best.