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[ned]

A drug is a molecule that has pharmaceutical applications. The molecule has long complex IUPAC name. Any company that manufactures and markets the molecule gives it their brand/ proprietary name.

But, I think every such drug molecule has a generic name. Somewhere it is called International Non-proprietary Name (INN) as recommended by WHO. Am I correct that every drug has a generic name or INN?

[wal49]

The vast majority do, I've never come across one that doesn't as far as I can remember. For example, things like Lipitor are called atorvastatin as a generic name and Prozac is otherwise known as fluoxetine. So yep, I think it's safe to say they all do.
I hope I helped :)