What is a TA called when he/she is in charge of organization?
First to answer your titular question:


  What is a TA called when he/she is in charge of organization?


Such a position does (in theory) not exist, as a TA as by definition supposed to "assist" somebody else and not run the show on her/his own (I am aware that this is not how it sometimes works in practice).

Generally, you need to keep in mind that title and scope of academic positions, especially regarding teaching, are quite different between US and Germany, so you will likely not be able to do an accurate 1-to-1 mapping. I would write "Wissenschaftlicher Mitarbeiter" in the CV and explain what you actually did. Translating it to english is prone to confusion.

If you write TA, people will underestimate your responsibility in the course, if you write something like lecturer, people may infer that you already had a faculty position and will be confused by the perceived mismatch with the rest of your CV.