Not my app, but looking at the code the "device name" is the only thing updated by the app. The 'device label' is not changed. I don't think there should even be a value for 'device label' unless the user sets one manually.
The device's display name will be the 'device label' unless it's blank and then it falls back to the 'device name' field.
BTW, Dom isn't on Hubitat anymore. I intended to take over that contacts group app but ended up just creating my own. I did re-use some of his code, but there's a bit more functionality in my app.
I do have the names of the app and child devices disconnected. The device name will match the app when created, but changing the app name afterwards will not change the device name.