Lastly, get rid of the HBO name, something that has been around since the 70’s.
At least Paramount was smart enough to keep the Showtime name when they merged it with P+.
They're not getting rid of the HBO brand name. It looks like they're going to drop "HBO" from the name of the streaming service, branding it as simply "Max." But the cable channel will still be called HBO and the content they produce for it still dubbed "HBO Originals." There will still be an HBO branded content hub inside Max. In a way, this move will help preserve the purity of the HBO brand, so that it does not get extended in the public's mind to include all the non-HBO content inside Max. (As all that decidedly non-premium Discovery/HGTV/Food/TLC stuff gets added into the app, it makes even less sense to have HBO as part of the overall streaming service's name.)
Meanwhile, Paramount is actually renaming their premium cable network from Showtime to "Paramount+ with Showtime" (an awkward moniker that no normal person will actually call it). The premium ad-free version of their streaming service will go by the same name, while the basic with-ads version will still be known as just Paramount+.
The differences between the two go deeper than just branding. WBD is not only keeping their internal HBO team intact, they've locked down its CEO Casey Bloys and his team for several more years, while increasing the money given to them for new content development.
Meanwhile, Paramount has decimated their Showtime team, with that service being largely absorbed into other parts of the company. Longtime Showtime CEO David Nevins saw this coming, I'm sure, which is why he left awhile back (and then lined up a private equity firm to try to buy Showtime from Paramount for $3 billion, an offer that the company turned down). Expect to see fewer Showtime Originals going forward, since Paramount+ Originals will take up some of the budget and airtime. And it looks like most of the Showtime Originals they produce will be endless franchise iterations of past hits. I used to love Showtime, although I've never cared for Paramount+. At this point, it looks like something I can cross off my list of services to juggle.