I don’t really have a new variant spelling of Trautvetter in this entry for Anna Catharina Trautvetter that appears in the records of Wohlmuthausen, Thuringen, Germany, in 1823. There’s not a “new name” of Trautvetterin.
The “in” is an ending attached to the name because Anna Catharina was female. Her last name is Trautvetter. Issues of this type are why it is important to learn about the culture and linguistic practices for the area where your family lived. What’s true in one area may not be true in another. Don’t assume an entire country is the same. My Germans who lived in other areas did not include any gender derived endings to surnames–ever.
But certain parts did. And other parts didn’t.