Hi, @Great_Iskander
According to your description, I tested it on my own computer, and at first there was rename the Internet next to the organizer in the network connection, but after I tried to change the name, the computer prompted me that I needed to change it as an administrator or as an authorized identity.
To modify the name and description of network connections, you may need use the Network List Manager Policies to allow users to change the network name and location.
Hope the information is helpful.
Best Regards,
Hania Lian