Would the following sentence be correct?
Anna Müller of German website "Utopia.de" wrote that...
Or would I have to use an article?
Anna Müller of the German website "Utopia.de" wrote that...
And if not, why?
Would the following sentence be correct?
Anna Müller of German website "Utopia.de" wrote that...
Or would I have to use an article?
Anna Müller of the German website "Utopia.de" wrote that...
And if not, why?
The short answer would be that you need the here because it is the website. You could use
Anna Müller of "Utopia.de" wrote that ...
because Utopia.de is a name.
You can see from the comments there are similar constructions where using the is optional, and the rules are not always clear. Even if the is optional it is still correct to add it, and my recommendation would be that you do so.