There's a name collision with https://en.wikipedia.org/wiki/Automat
Automat is a common European word for 'machine' or 'vending machine', many languages have it.
Only if the context in which you're writing/speaking is such that you are likely to be referring to a historical restaurant genre or whatever this thing is
Automat is a common European word for 'machine' or 'vending machine', many languages have it.