I wanted to report back on the answer here.
When you change a stage name in an approved model, you are simply changing the label. You accomplish this by editing the model, chosing the existing stage and in the Stage Properties (at the bottom) change the label.
When doing so, all references to that stage change automatically - this is across flow steps, filters and reporting. The old name is simply replaced with the new name. Existing metrics in RCE are not lost - they just appear under the new stage name.
I went ahead and did this to multiple stages in a model and reapproved and all worked as expected.
Note, this is *not* the same as creating new stages and/or merging exsiting stages together. In the case of merging stages, metrics will change and it will causing reporting to change.
Sheila