[balfirevic]

That doesn't sound like "inverting". If that is what it means then it is indeed a bad name.

I always thought it means making one of the leaf nodes a root of the tree. Physically, it would look like taking one of the leaf nodes with your fingers and "hanging" the tree off of it.

[BearOso]

Inverting means inverting the sort order. The easy answer is to encapsulate the tree in a new structure and add a Boolean flag called “inverted,” since you’re just reinterpreting the meaning of left and right children.

What you describe is called “rotation,” and is used to rebalance.

[boomlinde]

invert: to reverse in position, order, or relationship