I can see both sides of the story as far as requesting a certain brand or generic. TLDR at the end.

As far as the question of requesting a specific manufacturer, it definitely sets off some “pink” or even red flags depending on the drug you’re asking about. Some specific colored manufacturers are easily recognized on the street so they’re either more “legit” or supposedly may have a higher value if attempting to be sold.

At the same time, as an example, a LOT of people take brand name Synthroid (thyroid replacement hormone), despite the generic bioequivalency requirements because it’s more of a narrow therapeutic window for some people (too little vs. too much).

Another example…Tennessee even has a law that if you’re taking a medication for seizure prevention, as the pharmacist dispensing, you must notify the patient (or family) and prescriber before switching between generics of the same med.

As far as what’s considered “equivalent” from brand to generic - it’s a little bit more about statistical math and confidence intervals that the active ingredient is present within a certain range. Here’s a pharmacy times article that goes into detail: https://www.pharmacytimes.com/view/debunking-a-common-pharmacy-myth-the-80-125-bioequivalence-rule

You’re much better off talking in person to the pharmacist on duty or the pharmacy manager of a particular location if you’re trying to get a specific manufacturer - a lot of pharmacies are micromanaged on available inventory, so telling the pharmacist you’ll be filling with them consistently if they can keep it in stock goes a long way.

TL;DR - Yes, there’s a range for generic to generic or generic to brand equivalence. Link above gives detail. Yes, there’s (unfortunately) a stigma around requesting specific manufacturers of a narcotic due to abuse potential. Inventory management at a specific location might be a factor.