Is it possible to change the File name with the Common name in Model Tree?

If I want the PTC_COMMON_NAME parameter to match the file name of the model, I set it with a relation:

ptc_common_name = rel_model_name()

The only other way I've seen to directly change both of these is if I'm changing the name of the model only in the session. Otherwise, the PTC_COMMON_NAME parameter is protected from direct changes, likely since it plays  a part in Windchill?

The common name in Creo is for my understanding the opposite, The common name in Creo gives you the freedom to use any (wchar) character you want for your numbering system. On top you can use character which are not allowed to use for file names like ‘/:@‘ and so on. In Creo you can’t use a .+, as the first character as well for example.
The common name can be used to continue with your current numbering system. In my point of view you should use this. This may save a tremendous amount of money for your company. And as already mentioned, there is logic which may protect this parameter for further changes. 

If your company uses only a numbering system which matches the requirement for Creo file names, you should have a simple  notify function to sync this if possible.

If you are using Windchill: see https://www.ptc.com/en/support/article/CS245234 and keep in mind, that a Windchill connected Creo behaves different in some aspects.