Medication
For example, in the United States, the most common brand name for acetaminophen is Tylenol.  One of the companies that makes acetaminophen (Johnson & Johnson) chose the name "Tylenol" for its acetaminophen.  Another company that makes acetaminophen (GlaxoSmithKline) chose "Panadol" as its brand name.  Like with most medicines, there are many other brand names for acetaminophen.