Is there a name for a doctor that specializes in genetic disorders?

Clinical geneticist. Many geneticists are not medical doctors but are phds who conduct research, statistical analyses, & run clinical laboratories. Some, like me, see real patients & are called clinical geneticists. Biochemical geneticists concentrate on patients with metabolic problems. Genetic counselors, who are not physicians, assist clinical & biochemical geneticists & other doctors. Often it's a team effort.
Clinical Geneticist . Clinical geneticist or some say medical geneticist. This is a doctor with md degree who can diagnose and treat patients. Medical biochemical geneticist treats patients with inherited metabolic disorders. Dysmorphologist is a geneticist who sees patients with birth defects, but that is not an official degree, as dysmorphologists are also clinical geneticists.