Has "The history PhD" got the same meaning as "The PhD in history"
I don't understand the sentence. Like the Ph.D as a level of education in history?
Yes. "διδακτορικό δίπλωμα" or, informally, just "διδακτορικό" means "doctorate degree". Since PhD is the type of doctorate degree awarded in History, you get this translation.
I think "the history PhD" should be accepted
It's quite uncommon like that, whereas it's more often found in phrases like "the history Ph.D. student", "the history Ph.D. program" and so on ;)
Would "the doctorate of history" be accepted? Sounds more like what you would say?