what is the document called that gives medical decision rights e.g.: if comatose can terminate one's life?

An advance medical directive, or a living will, or a medical power of attorney.

Where I live, it is called a Medical Proxy.

Speak to your doctor, they or the hospital can provide you with the forms and the procedure to put it into effect.

Here in the UK, the only thing that can do that is a power of attorney, or an advance directive in the case of people no longer mentally capable of deciding for themselves. What country are you asking about?

Advance healthcare directive, also known as living will, personal directive, advance directive, medical directive or advance decision.

Advanced directive, power of attorney....has several names.

Living will, DNR - do not resuscitate.

Along with de witt, you may be thinking of informed consent.

There's an important point here. There are very few places where euthanasia is legal. You're probably thinking of advance directives, expressing a person's wish not to be kept alive in certain hopeless situations; or a medical power of attorney, which gives somebody else the authority to make treatment decisions. But neither of those allows anybody's life to be terminated. They only allow life-supporting treatments to be withdrawn, so nature can take her course.

Living will for others Power of attorney