The name update of the portsets did cause problems with the programs that were running at that time : I think problems with the firewall rulesets which use these portsets and therefore with the rules applications which use these rulesets.
As I am a bit obstinate I try again :
I disconnected my laptop from the internet
I update the name of the portsets
I revalidated the firewall rulesets
I reconnected my laptop to the internet
With this way of doing I had no problems.
Maybe I was lucky.
In general, if renaming of names or strings is implemented well then renaming should iterate throughout the whole program without causing renaming issues.
When a program makes copies of certain names or strings (so not referencing them) then things may break because the reference is gone after renaming a name or string.
I’m not sure how CIS handles renaming in general, maybe devs can shed some light on it.