Most Vacuum cleaners have an information label which tells you the make, model and serial number.

It also includes more technical data like Voltage, hertz, wattage, date of manufacture and type of insulation. 

Except for the earliest Dysons, later Models have white label with black text. 

Most vacuum cleaners will have a label similar to this, it's not always easy to find, sometimes it's under the cleaner, or behind the cyclone and bin/Bag section. Sometimes it is even behind the hose.