A virtuoso organ work…
The nickname, “Dorian”, is not from Bach. It is from the key signature used, which has no sharps or flats. The notes D E F G A B C D would be the Dorian mode. Bach’s music is clearly in D minor. He just chose not to put Bb in the key signature. There is another more famous “Toccata and Fugue in D minor” that everyone knows, and that one is linked to Fantasia. This one has the nickname “Dorian”.
Bach worked in Weimar between 1708 and 1717, during which he composed most of his organ works including BWV 538, and the truth is that no one knows exactly when he wrote this. I just used 1713 as a mid point of when it could have been written.