I don't know what to tell you. It's a "soda fountain" because it dispenses "fountain soda"; sometimes also more broadly "fountain drinks", as occasionally they also dispense non-carbonated drinks like lemonade or Hi-C. Fountain vs. bottled drinks being a standard distinction at fast food and some other restaurants I've encountered in the US and in Canada. It's been a while since my last trip to Europe, but I'm pretty sure they made the same distinction in Ireland in 2018 when I was there last.
Like I said, if you're in one of those regions that uses the term "pop" instead of "soda", "pop fountain" makes sense. "Pop machine" runs into the issue of confusing it with an automated vending machine.
It is funny when folks who don't possess vocabulary for a given object express disbelief that other people do. Like Morrus leaping to the assumption that Cadence was speaking from "very limited personal experience of the world" because
Morrus hadn't heard a term.