You can just ask the Pharmacy for brand name.. however your insurance may or may not cover it. If your Doctor thinks you have to have the brand name they can write "no substitutions" on the prescription with the brand name.. and you have a higher chance of the insurance company covering it. but they still can refuse. Also keep in mind the Pharmacy may not be able or willing to provide brand name depending on the drug and costs and the quantity your prescription is for. Brand name is generally much more expensive than generic and if they can't sell you the entire bottle they may not want to do it because it would be a loss for them in the long run. Even if the Pharmacy will provide you with the brand name if it is a drug that has been avail as a Generic for a while keep in mind they will likely have to order it in, they can usually get it the next business day however.
You can request brand name drugs when generic drugs don't work by asking your doctor or pharmacist. However, note that a pharmacist or doctor will not be able or willing to provide brand name. This is because of the type of drug and cost.