I favor your proposed phrase "psychological health" (if I understand correctly that is the wording you are suggesting).
While I don't have further ideas at this time for additional phrases, it is important to add to this discussion that 'psychological health' is not currently able to be measured, let alone resolved, by instruments in the way that physical health is in today's medical profession.
What seems key to the struggle to provide an apt label here is this: physical location/s currently cannot be scanned or clearly identified as an 'objective' source of the 'psychological illness', thus the medical profession cannot then use its current approach/es (pharmaceuticals, treatments (e.g., radiation) or surgery) to resolve or at least lessen the impact of the psychological turmoil. Therefore, current medical terminology comes up wanting.
Caveat: I know, as we all do, that research is ongoing, with advances in tools like TMS (transcranial magnetic stimulation), DBS (deep brain stimulation), pharmaceuticals and more (and, thankfully, the ceasing of the use of lobotomies and other such archaic surgical methods). https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3984894/
But I think those of us in this discussion would all agree that pinpointed, targeted, successful remedies remain elusive in our current medical profession, hence the difficulty in effectively naming this type of health struggle in words for something our society has yet to effectively understand and treat in the first place.
Does this help frame the struggle to find a more descriptive, and hence useful, name for what we are challenged with?
Indeed; accurate measurement is currently not achieved from what I can ascertain (current psychometric tools have significant flaws when viewed from different perspectives insofar as they don’t account for contributing symptomatology when it’s not psychological in origin, for one), and it’s clearly unmeasurable by current existing physical health measurement tools (hence why they aren’t reliably used from what I understand).
This is why I feel the proposal of nomenclature that aligns with demystification as well as specialty would be a robust foundation to start with, and then development of clear frameworks from there may indeed be developed (a different approach to the traditional methodologies that seem to mix organ heath and functional outcomes of brain function - something that doesn’t work because organ health doesn’t align with the functional outcomes/outputs of brain activity in many instances of psychological health concerns).
My sister uses deep brain stimulation to manage essential tremor that she was born with, however practitioner confusion as to whether this was structural or functional/psychological or even psychosomatic (🤦🏻♀️) made it even more evident to me that a classification system based on the unique functions and engagement in society (psychological health) as well as the structural status (organ health) was required.
While there is ‘muddy water’ between the understanding of what each do and how their function can impact a person and their opportunities in society, then we will falter in supporting people to the fullest extent.
As a side note, I also believe that taking a much more transparent, easily identifiable approach to organ/psychological health approaches, we can then develop much better means of assessment, interventions, and evaluation of support mechanisms including medications, psychotherapies, and self-supporting tools.
I don’t feel like the current mechanisms are working, and so we need a totally different approach from the ‘ground up’…and after seeing a friend very close to being subjected to ECT without her consent due to the systemic failures existing in Au (including the confusion regarding organ/psychological health perspectives and approaches), we - here, anyway - need a radically better system of approach to health treatment of what is currently called mental health.