So, a method that alters its object is a mutator. A method that does not alter its object but returns a value (or reference to a value) is a getter. Is there a widely used name for a method that does not alter its object, does not return a value, but potentially alters objects passed to it as arguments. That is, a method that would only every be called for its side-effects on the arguments.
These methods are quite common if you are keen on the Strategy design pattern.
The lack of replies suggests that, no, there is no widely used name for such a method.