I know that in many non-US countries they require identification to
check into hotels. However, in the United States I am not aware of any
laws that require this. Do they exist?
Yes:
According to Massachussets legislature:
Section 27. Every innholder, and every lodging house keeper required
so to do under section twenty-eight, and every person who shall
conduct, control, manage or operate, directly or indirectly, any
recreational camp, overnight camp or cabin, motel or manufactured
housing community shall keep or cause to be kept, in permanent form, a
register in which shall be recorded the true name or name in ordinary
use and the residence of every person engaging or occupying a private
room averaging less than four hundred square feet floor area,
excepting a private dining room not containing a bed or couch, or
opening into a room containing a bed or couch, for any period of the
day or night in any part of the premises controlled by the licensee,
together with a true and accurate record of the room assigned to such
person and of the day and hour when such room is assigned.
I would imagine that legal advice has been sought by hotels and that lawyers have suggested that hotels seek official identification in order to comply with this.
In Los Angeles, an ordinance specifically targets cash or walk-in guests:
- Renting of Hotel Rooms. The operator of a hotel shall not rent a room except in compliance with the following conditions. (a) A guest
who pays all or part of the rent for a room in cash at the time of
checking in, and a walk-in guest, shall be required to present an
identification document or a housing voucher at the time of checking
into the hoteL.
Also Tennessee has proposed a similar bill:
Hotels and Restaurants - As introduced, mandates lodging
establishments maintain a guest register providing the name, address,
date of birth, copy of a state or federally issued photo
identification and vehicle registration information of every guest
staying at the hotel; requires the hotel copy the photo ID; authorizes
law enforcement personnel to inspect the registration records for law
enforcement purposes.
Your next question:
I have had similar conversations at several different hotels. What is
going on here? Is there some secret law or something that hotels have
to record your identity in the United States?
I cannot find any evidence of any federal law regarding this and due to the other legislation found, it is unlikely that any exists that is not localised.
Maybe a better question would be: is it possible to check into a hotel
in the United States without a driver's license and credit card?
I would advise you to check the booking conditions of the hotel before you attempt to check-in, for example, the hotel you list states in their FAQ (bolded text is bolded question from hotel page FAQ):
Is my ID/passport required at check in?
Yes, a valid government
issued picture ID is required for Hotel Check-in.
and
What forms of payment are accepted to pay for my room?
A valid credit
card is required to check in to the hotel, but guests may use cash or
credit card at check-out to settle their bill.