I disagree with coining a different term to make it more socially acceptable. Therapist being generic is useful for keeping mental health issues under a single blanket and preventing other people from easily figuring out what you're going there for. This is similar to how going to a doctor could range from doing your yearly check up to following up on a possibly fatal issue.

The real solution is the one we've already been pushing for and have had a great amount of success over the years, which is to treat mental health issues with the same importance as physical health issues.