Usually, we refer to them as "Coke" mainly because most of the more popular brands of soft drink are indeed made by the Coca-Cola Company. Most of the time, the Pepsi company stuff is merely referred to by it's brand name.
But yeah, we use "Coke" as the generic term around here in West Texas usually, since most people do prefer Coke over Pepsi. :3
I personally hate it when people call it "Pop" or "Soda" because those are outdated terms. x3 (Seriously, unless the person is a senior citizen, I will almost always correct them.) I tend to use "Soft Drink" if I really have to refer to it without naming a specific brand.
People who call it "Carbonated Beverage" are just being smart-alecks so I ignore those people. xD