Yep, same here in Alabama. The conversation usually sounds like this :Pretty sure they still call it "tonic" in the old west part of Maine. Growing up in Atlanta we called any cola-looking soft-drink "Coke". There wasn't anything else.
"I'm going to the store, want anything?"
"Yeah, will you get me a coke?"
"Sure...what kind do you want?"
This may sound odd to the out-of-towners but a coke can mean any carbonated soft drink.