In most places some form of ID is asked for, but as a regular I am not asked repeatedly at same hotels. Even if one does not have ID, I doubt hotels are keen on making it a problem.

But, it would never be a good idea to try to stay under an assumed name. That is probably illegal in many places, and would be embarrassing if hotel figured it out. Staying under an alias would be something arranged in advance with management and security.

In true high profile situations, such as POTUS, hotel may not know who the guest is in advance. But, this does not seem to be the case, as anyone like that would have security people to take care of it, and would not be asking questions about it on this forum.