When discussed as a technical project it would be ‘Project SAFE’
As a point of general discussion, I tend to describe it as the internet with a prefix that conveys the meaning to the current audience i.e a safer internet, a private internet etc…
The internet definition fits and is the common name for what were using now, SAFE slowly takes over the infrastructure and we end up with a network as originally envisaged.
a global computer network providing a variety of information and communication facilities, consisting of interconnected networks using standardized communication protocols