It is a nickname by anorexics for Anorexia Nervosa. They refer to Ana as having a personality and in a way it is like they are trying to say that 'she' is watching and making them do it because she...
The name 'Anna' or 'Ana' is of Hebrew origin, and is a form of the name 'Hannah'. 'Hannah' means 'favoured grace'. The name 'Rose' is shared with the name of a flower, giving it a floral meaning.