when your doctor writes the prescription, if you need the brand name rather than the generic, he will write fill as written, which tells the pharmacist that it must be the brand name. the medication in the generic is the same as in the brand name, but the filler is different. generally the only time a doctor will do this is if the patient is allergic to a certain filler or for other health reasons.
It's likely that the name brand won't be covered. Name brand drugs (especially those used to treat mental health conditions), are sold at a premium to pad big pharmas pocket books. I've taken Bupropion before, and it's exactly the same thing.
Just because a doc writes a script for a brand name doesnt mean the insurance will pay for it. Generics are cheaper so if one is available many insurance groups wont pay for the name brand. Change insurance coverage is your best bet.