I think in CBS’s case the idea was to build an audience of younger viewers who could not only support a new streaming service (since they all know it’s the future) and also to avoid the brand drag that CBS can have. It’s not a “cool” network, by any means, and its overall audience skews older. They get huge numbers, obviously, including lots of young folks, but carving out a new, side identity is a thing now. And look at what they started with for exclusives. Discovery and The Good Fight.
Not saying it’s a good idea, necessarily, but I think the name-shift to Paramount+ is an extension of that. Sometimes running away from your own brand is intentional.