I do. I extend it beyond medicines as well. Corporations have spent lots of money for their brands to be household names. They don’t control my language.
Specifically to medicine, I will note that the generic name actually carries information that the brand name does nothing for. Lisinopril and enalopril are the same medication class, act similar. Amlodipine, nimodipine, nicardipene are all the same class. Those generic names have important meaning.