How do you choose a medical specialist when getting a referral?

My wife has a doctor's appointment coming up where she'd like to get a referral to an allergist. She has a specific one in mind that she'd like to see after working with another allergist a few years back that she had poor experiences with.

In previous referrals she's received (her OB for a high-risk pregnancy, the aforementioned allergist) she has had no input on who she has been placed with. However, she has heard about others that were able to choose their own OB, also for high-risk pregnancies.

So, is it as simple as just requesting a specific person? The allergist she would like to see has on their website that they don't do second opinions or transfer of care, but she hasn't seen her old allergist for four years now so we're not sure if that applies here. Referrals she's had for other things have only been good for a year or until the specific issue is seemingly resolved.

Obviously, she can just ask her family doctor at the appointment, but it'd be nice to know what the practice is beforehand if possible!

Thanks.