No. It doesn’t really matter. 

As long as its working properly. 

So, -- even though it does not matter- can it be changed- - its the ‘device details’ section of the Home Screen- under- ‘service provider’.

I do not see any option to change the service provider name in the app.  It is possible that factory resetting the modem and/or uninstalling/reinstalling the app could update from COX to Xfinity, but as plemans said, it doesn’t matter.  Also, both of those options are purely speculative as to changing the provider name in the app. Think of it as a cosmetic bug.  I would actually recommend not even using the app as it brings nothing to the table. The modem webpage is far more informative.