I usually use the name of the drug when there are multiple brands with trade names for it, or when there are trade-name drugs that use multiple formulations with different ingredients.
For example, famotodine is the active agent in Pepcid and Zantac. Omeprazole is sold as Prilosec and Losec. Acetaminophen is in Tylenol, Tempra, and Panadol
When I want Pseudoephedrine and not phenylephrine, they’re both branded under the trade name ‘Sudafed’ but only one of them really works for sinus pressure.
When I want Dextromethorphan or Guaifenesin (active ingredients in Robitussin) there are lots of other brands (Nyquil, dayquil, etc) that deliver them and knowing which drug is which and what part they do means I can pick which one to use if I don’t want the other one’s shitty side effects.
This is where windfall taxes come back into basic utility. Also it becomes the basis for antitrust action on price collusion if all the sellers coordinate