In my opinion, they'd be much more effective if they just killed the Bing brand, killed Bing rewards, killed the Bing newsfeeds, rebranded it to "Private Search" at privatesearch.com, and called it a day. Yes, people have memories shorter than a goldfish.
Agreed that the Bing brand has to go, but I think they should use their normal naming schemes, something like "Microsoft Azure Cloud Search Pro 2025 SP1"