Most drugs and medicines have more than one name. These include trade names or brand names that the manufacturer and distributor use. But there are also usually more than one "scientific" name, too.
Take for instance Bayer Aspirin. The brand name is Bayer. Only the trademark holder (Bayer AG) can sell aspirin under that name. The generic name is aspirin. Aspirin is a word in the dictionary and vendors can use the name aspirin when they sell that drug. A more scientific name is acetylsalicylic acid. An even more formal scientific name is 2-acetoxybenzoic acid. And there are more complex names. And there is a Chemical Abstracts Service number: 156865-15-5.
Everyone working at a healthcare facility needs to understand these naming conventions. The waste management plan should specify what names to use for the most widely used pharmaceuticals in the facility. What names will be used in manifests? What names will be used in spill logs and pharmaceutical inventory databases? What names (if any) will be used on storage containers? Develop and plan and stick to it.