Alexa identifies Dyson machines using their room name. The room name is set when you first connect your machine with the Dyson app and can be changed using the Link app as well. A list of pre-set room names are available in the Dyson Link app, such as 'Bedroom' or 'Kitchen'.
For convenience, you can also rename your machine using the Alexa app. However, this does not affect the room name in the Dyson Link app or how you control your machine with voice commands.
To control a specific Dyson machine using voice commands, you can either directly name the machine in your first command or wait for Alexa to ask which machine you are referring to.
If you ask "Alexa, enable auto mode on Bedroom.", Alexa will identify the 'Bedroom' machine and enable the auto mode for it.
If you ask "Alexa, enable auto mode.", Alexa will ask which machine you want to enable the auto mode for.