To rename your AirVisual Pro, you must be its owner and you must be logged in to the app or website with the email account that owns the monitor.
In the app, go to your Pro's page and click on the settings wheel in the top right corner. A browser will open and you can change the name inside the settings. Allow for couple of minutes for the device to refresh with its new name.
On the website, go to your profile tab on the top right corner, then click "My Devices"
Then select which device you want to rename, then click the settings icon beside "Share"
On the settings page, you can rename the device by changing the text in the "Device Name" then press "Apply Changes"