Legally herbalists are allowed to use any of those acronyms (CH, CMH, HHP, MH) in the United States as none of the abbreviations require any sort of education or certification. However please be aware that it is possible there could be some variation in different states and this answer may differ depending on the country.
Note that until completing clinical training of some kind, it would be misleading to call oneself a Clinical Herbalist or Master Herbalist. We do not confer any particular title on our graduates and we do not certify students and so using the title Certified Herbalist may also be misleading. We would encourage students not to represent themselves as clinical herbalists until they have hands on clinical training with a mentor.
Please review this article for further information: https://theherbalacademy.com/can-you-really-become-a-certified-herbalist/
Should you choose to study with us you may want to consider using Community Herbalist or Holistic Herbal Practitioner until after completing clinical training.