A Doctor of Philosophy, abbreviated as PhD, was an academic degree. Those with PhDs were addressed as "doctors", despite not typically having any connection to medicine.
This was an academic degree, as well, in the 29th century. Some of the bearers of this degree worked at the Temporal Integrity Commission. On the dedication plaque of the USS Relativity, Drs. R. Berman, P. Lauritson, R. Beltran, T. Russ, G. Wang, and J. Ryan were listed with this degree. (VOY: "Relativity", dedication plaque)
Background information Edit
As a psychiatrist – a medical specialist, unlike a psychologist – Dr. Dehner most probably had an MD as well. (This would be consistent with the many people today who hold doctorates in both medicine and a related field.)
While Dr. Dehner's degree was the only one explicitly referred to as a PhD, it seems likely that most non-medical doctors had PhDs. For example, Dr. Leah Brahms, Dr. Kila Marr, and Dr. Telek R'Mor were in professions (engineering, biology, and astrophysics, respectively) that, at least in "our" 21st century Earth, award the PhD for their doctoral/terminal degrees. The same is likely for other doctors who were clearly not physicians, such as Dr. Daystrom.
Dr. Dehner's file actually misspells the term, using P.H.D. rather than the correct PH.D. (Philosophy being one word)