Yes, it’s possible to do this. You may be surprised to hear that the USA is one of only two countries on the entire planet which it’s even legal to advertise drugs. All others outlaw it completely.
Indeed, that was surprising to hear, and a quick google search found me many countries in Europe where advertising drugs is legal, within some restrictive framework.
Both of those links say that there's a total ban on advertising prescription drugs to consumers, which is more specific than what the parent said but still very broad.
I’m sorry, yes, I should have specified prescription drugs, as that is what I meant. In context, though, this was what was discussed by the grandparent post: “[…] people go to their doctor asking for Rx by name […]”.
Before 1997 it was impractical to advertise them, though. You couldn't mention both the name of the drug and what it was for in an ad without including the entire warning label text. The deregulation was another Clinton thing, and its main beneficiary was the SSRIs.
I believe that's still the case -- which is why we get all those commercials with happy people having family moments while a voice in the background quickly announces "if you have experience any of the following symptoms head to the ER immediately."
