Premium Diet Concept for elderly european / german people 50+. Logo should always consist of two different colors that fit together. The name means: "The intuitive thin / slim and healthy formula". So the target group wants to be like that. Will be used for book covers so the aspect ratio should be like 2:1 or 3:1, rectangular size, that is important! The name has to be written down completely by integrating some kind of graphical element. The word "Die" could be much smaller, it is just an article and has no deeper meaning for the content. So maybe two lines all in all. The "&" is a "and" that connects the words "Schlank" and "Gesund". The logo / name should look good especially on white backgrounds.
You could inspire yourself by having a look at other commercial diets on market.