This example was doomed from the start because of this fact.
A lot of the US south uses the generic "coke."* It is not uncommon for this conversation to play out: "Can I get a coke?" "Sure, which kind?" "A Coke" (or a pepsi, or fanta)
In my neck of the woods we call it "pop" which always sounded strange to me in isolation.
* As famously depicted in the 2003 Harvard Dialect Survey.