A JD is a full doctoral degree. The only professional in society that can call him/her self a "doctor" are physicians. The more appropriate address for a PhD or a JD at the university is "professor" which by definition means a teacher (doctor) of the highest rank at the university.
The Juris Doctor degree (J.D. or JD), also known as Doctor of Law or Doctor of Jurisprudence (J.D., JD, D. Jur., or DJur), is a graduate-entry professional degree in law and one of several Doctor of Law degrees.