Nah, "hoover" is just your dialect. American here, grew up in CA, and I've never heard or said "hoover".
But yeah, I wouldn't say "vacuum" as a method of action unless you really drilled down. (Something about "pump" and "sucking", but I'd have to think for a bit to get to the actual physical "vacuum" aspect of it.)
I bet it would take along time for most people asked "how does a vacuum cleaner work?" to use the word vacuum, apart from as a name for the object.