PhD itself is an abbreviation for "Doctor of Philosophy." The title is more about the original Greek "lover of wisdom" than about the modern academic discipline of philosophy. https://en.wikipedia.org/wiki/Doctor_of_Philosophy
Doctor is similar - in the US, when someone says "Doctor" they usually mean "Medical Doctor" but "Doctor" just comes from the Greek "teacher" / "scholar" which is more broad and the title can still be used officially and correctly for PhDs. https://en.wikipedia.org/wiki/Doctor_(title)
Just a little correction. Doctor is Latin and roughly means "someone who has learned a lot."
Science also originally referred to knowledge. What we think of as "science" used to be called the natural sciences. Sometimes people get confused because I have a B.S. in Classics because science has lost that broader meaning.
Indeed, in the Summa Theologica, Thomas Aquinas asks if theology is a science, and concludes that it is. He also gave lip service to logical rigor and falsifiability, in the latter case by encouraging the discipline of asking contrary questions and answering them. What he didn't do was appeal to empirical data, to any great extent.
I think the reasoning behind "doctor of philosophy" may be lost to history. All knowing Wikipedia suggests that it didn't happen at once. My take was that the requirements for a modern PhD were added long after the title was adopted.
I suspect there was a time when a person could be well versed in multiple of what are now separated fields, and that you had to be a philosopher to make sense of science and math. Also, as science was flexing its own wings, claiming to be a philosopher might have been a way to gain an air of respectability, just like calling a physician "doctor" when the main impact of medicine was to kill rich people.
It is still called natural science, but it used to be called natural philosophy.
And it is interesting, as you say, that when it comes to Bachelor/Master/Doctor of Science/Art/Philosophy (even professor), these are all titles formed from arbitrary terms that have been enshrined by the institutions that give people these titles.
