You are correct in the fact that 'RasenBallsport' is the official name due to the Bundesliga's sponsorship reasons, but 'Red Bull' is still used colloquially. 'RasenBallsport' has always been a valid type-in. And I will heed your suggestions for 'Hoppenheim' and 'Vizekusen'.
I would be reluctant, as I've never heard it referred to as 'Union', but I think when one types 'Union' they understand what they're meaning, so I have changed the type-in.
Many are easy given a basic knowledge of German civic heraldry, like Augsburg, Munich or Frankfurt.
P.S: Maybe you can also accept Hoppenheim and Vizekusen