I am only familiar with the laws of OR, WA, MA, CA, and CO – the states where I'm considering doctoral programs – but "therapist" and "counsellor" are regulated and require one have a license to advertise with them. "Life coach" is the only title I am aware of that is completely unregulated across the US.

Psychoanalytical Therapist is perhaps the caveat you're thinking of? I know in New York it is a regulated title, and it may be possible to practice independently without a Counselling or Social Work degree provided one isn't billing insurance or advertising as a "psychotherapist".