didn't`you call this a HOOVER in the States ? I remember it from my youth in the 50ies and 60ies
I've never heard that term and I grew up in Minnesota. Could be a regional thing.
Common UK usage would be "hoover", & so this answer should be accepted in my view. I can't imagine anyone saying "vacuum" or "vacuum cleaner", & while "hoover" is a generic, "Dyson" specifically would mean an appliance of that brand.
we call it UN ASPIRATEUR in French.