On Corporate owned devices, the device name that is set in Sophos Central should update to the phone. However, the user should not be able to change the name on the device.
I'm also highly interested in this feature - for use in our on-prem installation. This feature is built into the iOS MDM Protocol since iOS 9 (for supervised devices). https://developer.apple.com/business/documentation/MDM-Protocol-Reference.pdf
To send a DeviceName command (available only on supervised devices or devices running macOS v10.10 or later),
the server sends a dictionary containing the following keys:
Content: The requested computer name and local host name for the device.
I'm used to this feature with a former MDM solution (AirWatch) and it was working like a charm. Now, with Sophos, we have dozens of "iPhone" devices and we're unable to set the name remotely. Of coure we do not want every user to name the device themselves.