MD is a state licensed designation required to practice medicine. It is unlawful to practice medicine without being licensed and it is unlawful to claim to be an MD without being licensed.
Hopefully, this quack, seditious wretch will get her due.
The regulations may vary from state to state.
AFAIK, “MD” is a degree earned by completing the courses and graduating from a 4 year medical school. Once earned, that “MD” is a designation that the individual carries for life. Similar to the D.O. degree from a college of osteopathy, “doctors” who now are recognized as physicians on equal footing with MDs in most if not all of the 50 states.
State licensing of “Doctors” is different. That indeed is required to actively practice as a “medical doctor” (diagnose/treat patients and bill for services) in each given state. The individual states determine exactly what credentials are needed for licensing. CA or OK or FL may be different than CT, for instance. I will leave out the bit about nurses (APRNs/DNPs) now being called “Doctors” too.
But a graduate of a medical school retains his/her right to identify himself as an MD (or DO) for life, and may use it for identification in public, after he has retired and is no longer licensed or no longer is actively practicing medicine.
As far as the AMA goes, it has little to do with the issue of licensing. It publishes magazines and makes public pronouncements. But only about 15% of the practicing physicians in the US belong to it any more. That has been true for decades.
In terms of this particular Yale psychiatrist, it is very odd that she no longer has a CT medical license. Unless she has given up treating patients at Yale, she would need one. It is possible that she has a license and practices in another state where the annual fee for the license is significantly lower than in CT (e.g., NY). If so, it is possible that she just has a legacy faculty title at Yale and visits there to lecture occasionally.