I am not sure if its possible. What are you actually trying to accomplish? Is this for device identification purposes for troubleshooting, or something else?

For all device platforms on Soti MobiControl, "device name" always refer to the private customizable name within MobiControl system (i.e. in web-console, device agent, script, logs, etc.) for identifying the device of interest. 

The name  configurable by end-user in Device's Setting that you refer to is called Personalized Name on Apple device platform.  Equivalent entity on Android platform conventionally is not configurable by MDM software, except for a very very small number of brand with OEM specific proprietary API callable with specific Android+ device agent.

On Android-Enterprise platform, Google seems to have recently defined a "standard" way for MDM/EMM software  to configure such entity, namely

    writesecuresetting -glo device_name  MY_NEW_NAME

However, whether or not this work depends very much on your device brand/model.  This command is from some Google online document which seems to be still evolving from time to time.  I reckon the situation should get better in 1-2 years' time after the standard stuff gets frozen and implemented in most AE-compliant device firmwares.

The software from the customer requests this name, so it needs to be different on every device.
Therefor it would've been nice to have a script or something we can send instead of manually editing it.

Its also used in lockdown template (%PERSONALIZED_DEVICE_NAME%), so users can see this and recognize it.

I have the same necessity with Zebra devices.

Customer would like to read the device name directly from lockdown screen.

I tried the script suggested by Ray but it doesn't work into Android 11.