I don't have experience with this particular scenario, but I would be surprised if the UAE/Dubai government took any action if you moved hotels; they wouldn't even have any way to notice, unless the expiration date of the visa is scheduled as the day that you check out of the hotel.

On the other hand, hotels often (and are probably supposed to) ask to see your visa when you check in, so if you present a visa indicating your sponsorship as another hotel, they might give you trouble.