It’s the insurance companies (Specifically the Pharmacy Benefit Managers) who generally mandate the brand name over the generics. Prescribers might write the brand name on the prescription, but most (if not all) states have laws that allow automatic substitution to the generic.
Pharmacists (Who generally do not do any prescribing*) and Prescribers don’t get any benefits from prescribing brand names. If they do, they’re likely breaking anti-kickback laws.
(*There are clinics and states that allow pharmacists to prescribe medications. In Oregon for example, retail pharmacists can prescribe birth control. Or a clinic may have pharmacists reviewing and adjusting a patient’s warfarin therapy)