I would assume that you could ask to be referred to a specific doctor. When my Neurologist said he was going to refer me to a pain management doctor I asked for a specific one and he did it. Only reason I asked is because I wanted one closer to home. Can't hurt to ask...
I would definitely ask for one that has a lot of experience.... That's how I found my current primary care physician. I called several and asked if the doctor had any experience with peripheral neuropathy (he did) and they even told me the number of patients he had with peripheral neuropathy. My long time primary care physician had no clue about neuropathy so I changed. I have
peripheral neuropathy and
radial neuropathy.
With my health insurance plan, it does not require referrals but most specialists do.