Well, it does literally say 'Alfred Dunhill's The White Spot' (with different formatting and such, of course). So, yeah, they do literally say 'Dunhill', albeit not as centrally as they used to.
Whether one thinks this is dumb is fair game of course, but they deemphasized 'Dunhill'; they didn't eliminate it from the stamping (though they often have, I would argue regrettably, in other marketing material).
Sykes
The reason for this is that Dunhill is now an international fashion and accessory brand, like Burberry, Gucci, etc. The business wants to disassociate itself as far as possible from smoking, which in the UK and the EU is seen as a negative and could even have compliance, financial and taxation consequences (the promotion of tobacco consumption, etc). This is very sad in the case of Dunhill - a company whose history is wreathed in tobacco smoke. This is why they divested their tobacco business to Peterson and the cigarettes and cigars to British American Tobacco. The pipes are still made by Dunhill at their Walthamstow factory, but they don't exactly shout about them and the name has been changed to Alfred Dunhill's White Spot Pipes to disassociate them from the "Dunhill" corporate logo. At least the Dunhill name is still there, although more obliquely than before. And at least Dunhill are still making their pipes - so the pipe business must still be of some importance to them, even if it's nostalgia and respect for the history of the company.
I remember in the late 90's at the Dunhill flagship store in Jermyn Street, London, pipes were given pride of place on a special mezzanine level, with leather smoking chairs and the "My Mixture" bespoke blending service, which was available back then. Those glory days are long gone. I believe Richard Dunhill was still running the business then, and the pipe and smoking division was very important to him and the history of the company. At Dunhill's current London flagship store, in Mayfair, the pipes are in the basement.
Interestingly, when I was in their Mayfair store looking at the pipes about 6 years ago a Dunhill company representative was showing off the pipes to a large group of Chinese visitors. She was boasting about the excellence of Dunhill pipes and how central they are to the history of the company, and that's encouraging.