PhD students and PhD researchers are not the same thing.
A "PhD researcher" is a researcher who has a PhD, while a PhD student is working on a project in order to obtain a PhD (i.e. does not have the degree yet).
I agree with you, that the term "PhD student" in English is rather unfortunate - in reality, it is much closer to an apprenticeship, as you are training to perform research. And you do this by performing research under guidance.
Other languages have separate words for people doing a PhD, e.g. "Doktorand" in German, which give less of an impression of "studentship". In English, this is (AFAIK) not possible, and the closest I can think of is "PhD candidate".
If you just would like to avoid the term "student" on a CV because you believe that it could be misinterpreted by people outside academia, I would instead refer to something along the lines of e.g.
"PhD project (in SUBJECT)"
"PhD research project"
This still covers what you have done, but avoids giving the job title you feel is ambiguous.
Making up new "job titles", especially if they can be misinterpreted, is not a good idea, as unilateral "bug fixing" of a language does not work: communication requires both parties to buy into the premise. In the best case, you will create confusion, in the worst case you will be guilty of fraud.