I have seen some of the PhD holders sign as "Dr. [First Name] [Surname], PhD".
Is it academically correct to write "Dr. Frank Amoani Arthur, PhD"?
There are two important points to note about name markers that refer to academic titles:
These two observations make the suggested name form Dr. Kay Doe, PhD rather ambiguous.
Does it refer to a person with two doctor titles because there are two markers? Or do both markers refer to just one doctor title? But if so, why is that doctor referred to twice in one name? This may even lead to suspicion: Does the name bearer use two markers which refer to the same title with the intention to sound more impressive than their academic distinction actually warrants?
This ambiguity is avoided if you use only one title marker per title.
I'm sure this must have been dealt with in previous questions, but the short answer is:
This is correct if you are both a medical doctor and an academic doctor. But just being an academic allows you to write Dr. (name) XOR (name) PhD.
In the US, at least the title doctor doesn't imply a medical doctor, though it includes that. My students would usually refer to me as Dr. Buffy. Someone not knowing that I hold a doctorate might call me Mr. Buffy, but Dr. Buffy is more specific.
If I wish to list my degrees after my name they aren't being used a title like Dr. or Ms.
So, being pedantic: Dr. Buffy, BA, MA, PhD. is just fine. In Germany, and places with a related academic culture, degrees are used more as titles so it is a bit different: Herr Doctor Professor Buffy.
Medical doctors (again in the US) insist on being called Doctor and have no difficulty with Dr. Foobar, MD. It would be extremely uncommon for them to be listed any other way.
Dr Jones if he has a medical degree. Mark Jones, Ph.D. or Dr. Jones, if he has a Ph.D. Never Dr. Jones, Ph. D.
If you have Dr. NAME only it might cause some confusion. I was once caught in a situation where I was asked to be on standby for assistance during a medical emergency because my boarding pass identified me as Dr. MYNAME. I had to explain that the Dr was for a PhD and not for medical practises. In my opinion the academic the title should be Dr. LASTNAME or Dr. LASTNAME M.D. for a medical practitioner Dr, LASTNAME PhD for an academic qualification Dr. LASTNAME HC for an honorary doctorate (honororium causa)