I agree with you about the word psychoanalysis. If used precisely, it refers exclusively to Freud's system. That is why Jung coined the term Analytical Psychology, in order to distinguish his method from Freud's. I use it, however, in order to avoid having to give long explanations along those lines. All I mean by it is 'analysis of the psyche', without intending to refer to any specific person's system.

My preferred term would be psyche-analysis, which is neutral, but as that would be something I've invented myself, no-one else is going to immediately understand my intention.