An ADHD diagnosis needs to be done by a neuropsychologist, who usually has a Ph.D. and specific board certifications. An anxiety disorder diagnosis is usually done by a psychiatrist, who is a doctor with an M.D. and specific psychiatry certifications.
There are several types of professionals who typically diagnose ADHD. These include: physicians (especially psychiatrists, pediatricians, neurologists), psychologists, social workers, nurse practitioners, and other licensed counselors or therapists (e.g. professional counselors, marriage and family therapists, etc.). [1]
Some examples of professionals who are capable of diagnosing ADHD include: pediatricians, psychiatrists, family physicians, nurse practitioners, psychologists, psychotherapists. [2]
I agree that it's both broader and more complicated than what I wrote. At least in some states in the U.S., a neuropsychologist can diagnose ADHD, but can't write prescriptions for medications to treat it. Meanwhile, a psychiatrist can write prescriptions for a patient with ADHD, but might only do so after he reads a diagnosis from a neuropsychologist. Your experience may vary.
Also, diagnoses for disability accommodations (e.g., in education) are a whole different and complicated thing.
That makes sense to me. Of course, I'm not disputing the existence of specialists. A nurse practitioner or pediatrician may not have the most familiarity or want to deal with the issue.