I'm constantly saying: Google it! Do you say that? And do you 'do' that--use Google to search for things? In the past, yes, I used Google a lot. Probably daily. However, I've recently changed to Duck, Duck, Go as my search engine. But I still tend to tell people to 'google' whatever it is.
I think 'google' has become the generic term for search engines--just like 'kleenex' is generic for any tissue. I use Puffs--have for many years. But I still catch myself asking for 'kleenex' at times.
I think it's the same thing for Coke. I don't know for sure, but I believe Coca-Cola might have been the first popular soft drink. My mom loved it; on the other hand, Grandma showed me that 'coke' could clean rust off an old child's 'highchair'! Personally, once I tasted Pepsi, I decided I liked it better than Coke.
Of course, brings up the question: what do you call Coke, Pepsi, Mountain Dew, etc? I say soft drink. But that's off topic!