You don't have to be concerned as a mental care worker/academic that you need give up the phrase "mental health." It's true, it's totally ingrained. The thing to do is Just shift your own perspective and mindset going forward to "mental care."
Example 1: Answer questions relating to mental health with the question: "What system of mental care would address that problem?"
For example:
Person A: We have to focus on mental health in this country!
You: I agree, what kind of mental care systems should we be proposing?